Analitical Reasoning

Analytical Reasoning The Resource Center

Types of Reasoning Conditional Map Assignments The Resource Center

Rule Symbols A radio station will air programs A,B... F, Monday through Friday, with the following restrictions The Resource Center

Program A must be aired before Program B A→B

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Programs C and D must be aired on consecutive evenings C↔D The Resource Center

Program E can not be aired on the second day. M

T ~E

W

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T

F

If Program A is aired, then program B must be aired A⇒B The Resource Center

If Program A is aired, then program B must not be aired A ⇒ ~B

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Rules Quiz If A ⇒ B, then B ⇒ A? Not necessarily If A ⇒ B, then ~B ⇒ ~A? Yes The Resource Center

If A and B are both aired, then C cannot be aired. A & B ⇒ ~C

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If C is aired, either D or E must be aired. C⇒D/E

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Either A or B must be aired, but they both cannot be aired. A / B ⇒ ~ B / ~ A, Either must

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Conditional Games

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Athletes in a meet If A competes, B must compete. If B and C compete, D cannot compete. If C and D both compete, F cannot compete. The Resource Center

Athletes in a meet If D competes, either E or G must compete. Either E or F must compete, but they cannot both compete. E and G cannot both compete The Resource Center

Symbolize clues 1. A ⇒ B, ∴~B ⇒ ~A 2. B & C ⇒ ~D, ∴ D ⇒ ~ (B & C) 3. C & D ⇒ ~F, ∴ F ⇒ ~ (C & D)

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Symbolize clues 4. D ⇒ E / G, ∴ ~E / ~G ⇒ ~D 5. E ⇒ ~F, F ⇒ ~E, Either must 6. E ⇒ ~G, ∴ G ⇒ ~E The Resource Center

If only 3 compete, which could be that group? (A) A, B and C (B) B, E and G (C) B, E and F (D) C, D and E (E) C, D and F

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• A, B, C. • B, E, G • B, E, F • C, D, E • C, D, F

Either E/F must. E ⇒ ~G E ⇒ ~F, Right C & D ⇒ ~F The Resource Center

If D & G both compete, what must be true? (A) C competes. (B) E competes. (C) F competes. (D) A does not compete. (E) B does not compete. The Resource Center

Map Quizzes

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1. Messages can be sent in either direction between G & H, J & M, and K & L. 2. Messages can be sent from F to K, from H to J, from K to G, from M to F, and from M to H. The Resource Center

Step 1 - Draw the map Using statement 1 G

H

M

J

K

L The Resource Center

Using statement 2

F

G

H

M

J

K

L The Resource Center

Which terminal can transmit to the greatest number of terminals? M

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In traveling from G to K, how many terminals other than G & K are involved?

F

G

H

M

J

K

L The Resource Center

Assignment games

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Six books — on History, English, Algebra, Ceramics, Spanish, and Philosophy — are arranged on a shelf, with a bookend at either end. The Resource Center

The History book is next to a bookend. The English book is next to the Algebra book. At least one book separates the English and Ceramic books, and the English and Spanish books. The Resource Center

The Ceramics book and the Spanish book are next to each other. At least two books separate the English and Philosophy books. The Resource Center

Step 1 - Framework End

1 2 3 4 5 6 End

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Step 2 - Symbolize the clues 1. Bookend ↔ H 2. E ↔ A 3. NOT E ↔ C, NOT E ↔ S 4. S ↔ C 5. NOT E ↔ P, NOT E – P The Resource Center

If H is next to E, what must be true? (A) P is next to a bookend. (B) C is next to a bookend. (C) S is next to A (D) P is next to C (E) A is next to C The Resource Center

put History next to either of the bookends End

1 2 3 4 5 6 End H

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History book is next to the English book End

1 2 3 4 5 6 End H E

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E↔A End

1 2 3 4 5 6 End H E A

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NOT E ↔ P, NOT E – P End

1 2 3 4 5 6 End H E A S/C

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S↔C End

1 2 3 4 5 6 End H E A S/C C/S

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Only book that remains is P End

1 2 3 4 5 6 End H E A S/C S/C P

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Which of the following books can be next to a bookend? I. Philosophy II. English III. Ceramics The Resource Center

Assignment - 2 D Grid

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On a train the staff were the guard, the TC and the driver. Their names listed alphabetically are A, B and C. There are also 3 passengers with names Mr. A, Mr. B and Mr. C. The following facts are known: The Resource Center

Mr. B lives in Delhi The guard lives halfway between Chandigarh and Delhi Mr. A earns exactly Rs. 200,000 a year. C once beat the TC in snooker. The Resource Center

The guard’s next door neighbor, one of the three passengers mentioned, earns exactly three times as much as the guard The passenger living in Chandigarh has the same name as the guard. What is the driver’s name? The Resource Center