Examples To Accompany Http://www.scribd.com/doc/16033954/algoppr-rev (19or24p Rev)
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Examples To Accompany Http://www.scribd.com/doc/16033954/algoppr-rev (19or24p Rev) as PDF for free.
More details
- Words: 5,376
- Pages: 7
19 or 24 Categorical Syllogisms Table Name 1 bArbArA 2 cElArEnt 3 dArII 4 fErIO 5 cEsArE 6 cAmEstrEs 7 bArOcO 8 fEstInO 9* dArAptI 10 dAtIsI 11 dIsAmIs 12* fElAptOn 13 bOcArdO 14 fErIsOn 15* brAmAntIp 16 dImArIs 17 cAmEnEs 18* fEsApO 19 frEsIsOn 20* (from 1) 21* (from 2) 22* (from 5) 23* (from 6) 24 (from 17) *requires existential import (EI) for validity
1
2
3
4
5
6
7
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 1 0 0 1 1 0 0
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∀ 1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
Q => ~R FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
∀
∀
∀
∀
∀
∀
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ P => R TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
∃ P^Q TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∃ P^Q TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ P => ~Q FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∃ P ^ ~Q FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE
∀ P => R TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
13
14
15
16
17
18
19
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 2 3 4 5 6 7 8
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
1 1 0 0 1 1 0 0
∃
1 2 3 4 5 6 7 8
∀ P => ~R FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
1 1 1 1 0 0 0 0
1 2 3 4 5 6 7 8
∀ P => ~R FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
R
1 2 3 4 5 6 7 8
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃
Q
1 2 3 4 5 6 7 8
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃
P 1 2 3 4 5 6 7 8
∀ P => ~Q FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∃
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃ 1 0 1 0 1 0 1 0
Q ^ ~R FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE
1 0 1 0 1 0 1 0
Q => ~R FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
1 0 1 0 1 0 1 0
R^Q TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
∀
∀
∃
∀
∀
∀
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∃ Q^P TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∀ Q => ~P FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∃ Q^P TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∀ P => ~R FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
8
9
10
11
12
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 1 0 0 1 1 0 0
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∀ 1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
Q^R TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
1 0 1 0 1 0 1 0
Q => ~R FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
∀
∀
∃
∀
∃ P^Q TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∃ Q^P TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
20
21
22
23
24
1 1 1 1 0 0 0 0
1 2 3 4 5 6 7 8
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
R
1 2 3 4 5 6 7 8
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃
Q
1 2 3 4 5 6 7 8
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃
P 1 2 3 4 5 6 7 8
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∀ 1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
Q => ~R FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
∀
∀
∀
∀
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ P => ~Q FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ Q => ~P FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P => ~R FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
∃
∃
∃
∀
∀
∀
∃
∃
∃
∃
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P => Q 1 1 0 0 1 1 1 1
P => R 1 0 1 0 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q ^ ~R 0 1 0 0 0 1 0 0
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∃
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => R 1 0 1 0 1 1 1 1
P => ~Q 0 0 1 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
Q^P 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P^Q 1 1 0 0 0 0 0 0
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∃
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
P^Q 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R^Q 1 0 0 0 1 0 0 0
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∀
∀
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => ~P 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P => ~Q 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∃
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P ^ ~Q 0 0 1 1 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
Q^P 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
13
14
15
16
17
18
19
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
8
9
10
11
12
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P^Q 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P => Q 1 1 0 0 1 1 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
Q^P 1 1 0 0 0 0 0 0
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P => ~Q 0 0 1 1 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∃
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q^R 1 0 0 0 1 0 0 0
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => ~P 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
20
21
22
23
24
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
∃
∃
∃
∀
∀
∀
∃
∃
∃
∃
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P => Q 1 1 0 0 1 1 1 1
P => R 1 0 1 0 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q ^ ~R 0 1 0 0 0 1 0 0
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∃
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => R 1 0 1 0 1 1 1 1
P => ~Q 0 0 1 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
Q^P 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P^Q 1 1 0 0 0 0 0 0
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∃
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
P^Q 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R^Q 1 0 0 0 1 0 0 0
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∀
∀
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => ~P 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P => ~Q 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∃
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P ^ ~Q 0 0 1 1 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
Q^P 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
13
14
15
16
17
18
19
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
8
9
10
11
12
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P^Q 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P => Q 1 1 0 0 1 1 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
Q^P 1 1 0 0 0 0 0 0
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P => ~Q 0 0 1 1 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∃
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q^R 1 0 0 0 1 0 0 0
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => ~P 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
20
21
22
23
24
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 1 0 0 1 1 0 0
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∀ 1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
Q => ~R FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
∀
∀
∀
∀
∀
∀
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ P => R TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
∃ P^Q TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∃ P^Q TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ P => ~Q FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∃ P ^ ~Q FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE
∀ P => R TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
13
14
15
16
17
18
19
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 2 3 4 5 6 7 8
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
1 1 0 0 1 1 0 0
∃
1 2 3 4 5 6 7 8
∀ P => ~R FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
1 1 1 1 0 0 0 0
1 2 3 4 5 6 7 8
∀ P => ~R FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
R
1 2 3 4 5 6 7 8
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃
Q
1 2 3 4 5 6 7 8
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃
P 1 2 3 4 5 6 7 8
∀ P => ~Q FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∃
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃ 1 0 1 0 1 0 1 0
Q ^ ~R FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE
1 0 1 0 1 0 1 0
Q => ~R FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
1 0 1 0 1 0 1 0
R^Q TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
∀
∀
∃
∀
∀
∀
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∃ Q^P TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∀ Q => ~P FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∃ Q^P TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∀ P => ~R FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
8
9
10
11
12
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 1 0 0 1 1 0 0
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∀ 1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
Q^R TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
1 0 1 0 1 0 1 0
Q => ~R FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
∀
∀
∃
∀
∃ P^Q TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∃ Q^P TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∀ Q => P TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
20
21
22
23
24
1 1 1 1 0 0 0 0
1 2 3 4 5 6 7 8
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 2 3 4 5 6 7 8
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
R
1 2 3 4 5 6 7 8
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃
Q
1 2 3 4 5 6 7 8
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃
P 1 2 3 4 5 6 7 8
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∃
∃
∃
P
Q
R
1 1 1 1 0 0 0 0
1 1 0 0 1 1 0 0
∀ 1 0 1 0 1 0 1 0
Q => R TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
1 0 1 0 1 0 1 0
Q => ~R FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
1 0 1 0 1 0 1 0
R => ~Q FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
1 0 1 0 1 0 1 0
R => Q TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE
∀
∀
∀
∀
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ P => ~Q FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∀ P => Q TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
∀ Q => ~P FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
∃ P^R TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P ^ ~R FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
∃ P => ~R FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
∃
∃
∃
∀
∀
∀
∃
∃
∃
∃
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P => Q 1 1 0 0 1 1 1 1
P => R 1 0 1 0 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q ^ ~R 0 1 0 0 0 1 0 0
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∃
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => R 1 0 1 0 1 1 1 1
P => ~Q 0 0 1 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
Q^P 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P^Q 1 1 0 0 0 0 0 0
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∃
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
P^Q 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R^Q 1 0 0 0 1 0 0 0
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∀
∀
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => ~P 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P => ~Q 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∃
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P ^ ~Q 0 0 1 1 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
Q^P 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
13
14
15
16
17
18
19
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
8
9
10
11
12
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P^Q 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P => Q 1 1 0 0 1 1 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
Q^P 1 1 0 0 0 0 0 0
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P => ~Q 0 0 1 1 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∃
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q^R 1 0 0 0 1 0 0 0
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => ~P 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
20
21
22
23
24
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
∃
∃
∃
∀
∀
∀
∃
∃
∃
∃
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P => Q 1 1 0 0 1 1 1 1
P => R 1 0 1 0 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q ^ ~R 0 1 0 0 0 1 0 0
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∃
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => R 1 0 1 0 1 1 1 1
P => ~Q 0 0 1 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
Q^P 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P^Q 1 1 0 0 0 0 0 0
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∃
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
P^Q 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R^Q 1 0 0 0 1 0 0 0
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∀
∀
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => ~P 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
∃
∃
∃
∀
∀
∀
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P => ~Q 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∃
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P ^ ~Q 0 0 1 1 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
Q^P 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
13
14
15
16
17
18
19
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
8
9
10
11
12
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P^Q 1 1 0 0 0 0 0 0
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
P => Q 1 1 0 0 1 1 1 1
P^R 1 0 1 0 0 0 0 0
∃
∃
∃
∀
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∃
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => R 1 0 1 1 1 0 1 1
Q^P 1 1 0 0 0 0 0 0
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
P => ~Q 0 0 1 1 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∃
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q^R 1 0 0 0 1 0 0 0
Q => P 1 1 1 1 0 0 1 1
P^R 1 0 1 0 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => ~Q 0 1 1 1 0 1 1 1
P => Q 1 1 0 0 1 1 1 1
P ^ ~R 0 1 0 1 0 0 0 0
∃
∃
∃
∀
∀
∃
∃
∃
∃
∀
∀
∃
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
Q => ~R 0 1 1 1 0 1 1 1
Q => P 1 1 1 1 0 0 1 1
P ^ ~R 0 1 0 1 0 0 0 0
P 1 1 1 1 0 0 0 0
Q 1 1 0 0 1 1 0 0
R 1 0 1 0 1 0 1 0
R => Q 1 1 0 1 1 1 0 1
Q => ~P 0 0 1 1 1 1 1 1
P => ~R 0 1 0 1 1 1 1 1
20
21
22
23
24
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Related Documents
Study Guide To Accompany
June 2020 4
Examples
June 2020 21
Examples
October 2019 40
Examples
December 2019 35
