Lab Math 01

LAB MATH 001

(d) (1z1)z(1z1) + (1♣2) + (2z0) (e) (2♣2) × (2z5) L 7. Si K H = K+H+1 H+1 ; entonces calcular: L (a) 4 2 L L (b) (2 1) 2

Prof. Rensso Chung [email protected] Trujillo-Per´ u-Enero 2009 1. Calcular:

(c)

L

2L5 5 2

(a) 22 + 32 + 42 + 52

(d) (2

(b) 32 + 40 + 52

(e) (1

2

5

(c) 7 + 2 + 3

3

L L

2)2 + 2 L L 5) (5 2)

8. Si F (x) = x2 + x + 1; entonces calcular:

2. Si A?B = A2 +B 3 +(A+B)2 ; entonces calcular:

(a) F (2) + F (1)

(a) 3 ? 2

(b) F (3) + F (0) + 2

(b) (2 ? 2) + (2 ? 3)

(c) F (3) − F (2)

(c) (4 ? 2)2 + (3 ? 0)

9. Si X −→ Y = (Y + X)2 + X 2 ) + Y 3 ; entonces calcular:

3. Si a¥b = (a + b) × (a − b); entonces calcular:

(a) (3 −→ 2) −→ 1

(a) (7¥3) + (5¥2)

(b) (2 −→ 2) −→ (2 −→ 3)

(b) (2¥1)2 × (2¥1)3

(c) (2 −→ 4)2 + (3 −→ 0)

(c) (5¥2) ÷ (3¥1)

(d)

(d) (5¥1)3 − (2¥1)2

(e)

4. Si p ° q = (p + q + 1) × (p − q); entonces calcular:

5−→2 4−→2 2−→0 2−→2

+

1−→2 4−→2

10. Resolver 5x + 5 = 30.

(a) (5 ° 2)2 + 1

11. Resolver (22 )x − 4 = 12.

(b) (4 ° 2) ° 1

12. Resolver 100y + 200 = 400.

(c) (3 ° 2) ° (2 ° 1)

13. Resolver 7z − 9 = 49.

5. Si xNy = xy + x + 1; entonces calcular:

14. Encontrar el conjunto soluci´on de:

(a) 2N2

(a) 2x + 1 < 3

(b) (3N2) × (4N2) + 2

(b) 4x + 5 > 13

2

(c) (4N2) + (1N2) + (9N0)

(c) 7x − 7 ≥ 14

6. Si Y♣Z = Y 2 + Z 2 + 2Y + 2Z y YzZ = (Y + Z + 1) + (Y + Z)2 ; entonces calcular:

(d) 10y + 5 > 15 (e) 12z − 2 > 10

(a) (2z2) + (3♣2)

(f) 2 + 6z ≤ 14

(b) (2♣2)z2

(g) 14x + 10 > 38

(c) (3z2)♣(2♣3) + (2z2)2

(h) 10x + 10 > 110 1

(l) (Y ∩ Y ) − (X ∪ Y )

15. Si A = {2; 5; 7; 8; 10} y B = {2; 3; 7; 12}; entonces encontrar:

(m) (X ∪ ∅) ∩ (Y ∩ ∅) (n) (X ∪ Y ) ∩ (Y ∪ X) ∪ (X ∩ Y )

(a) (A ∩ B) ∪ A (b) (B ∪ A) ∩ (A − B)

19. Sea G = {1; 3; 5; 7} y H = {2; 4; 5}. Encontrar:

(c) (A − B) ∩ (B − A)

(a) n(G)

16. Si M = {a; b; c; d; e} y N = {a; b; f ; h}; entonces encontrar:

(b) n(H) (c) P (G)

(a) M − N

(d) P (H)

(b) N − M

(e) n(G ∪ H)

(c) (M ∪ N ) ∩ (N − M )

(f) n(G ∩ H)

(d) (M ∩ N ) − M

(g) P (G ∩ H) (h) P (G ∪ H)

17. Si P = {x ∈ N : 2 < x < 8} y Q = {x ∈ N : 2 ≤ x ≤ 5}; entonces encontrar:

20. Sea V = {x ∈ N : 3 < x ≤ 6} y W = {x ∈ N : 3 ≤ x ≤ 5}. Encontrar:

(a) P ∪ Q

(a) n(V )

(b) P ∩ Q

(b) n(W )

(c) P − Q

(c) P (V )

(d) Q − P

(d) P (W )

(e) (P − Q) ∪ (Q − P )

(e) n(V ∪ W )

(f) (P − Q) ∩ (Q − P )

(f) n(V ∩ W )

(g) (P ∪ Q) − (P ∩ Q)

(g) P (V ∪ W ) (h) n(V − W )

18. Si X = {N; ¥; ¨} y Y = {N; F; ¨}; entonces encontrar:

(i) n(W − V ) (j) P (W − V ) N L J N 21. Sea O = { ; } y L = { , }. Encontrar:

(a) X ∪ Y (b) X ∩ Y (c) X − Y

(a) n(O) + n(L) + n(L ∪ O)

(d) Y − X

(b) n(P (O)) + n(P (L))

(e) (X ∪ Y ) − (Y ∩ X)

(c) n(L ∪ O) + n(L − O)

(f) (X ∩ Y ) − (Y ∪ X)

(d) n(L − O) + n(L ∪ O) + n(O ∩ L) + n(P (L))

(g) (X − Y ) ∪ (Y − X)

(e) [n(O)]2 + n(L)

(h) X ∪ (Y ∩ X)

(f) [n(L)]2 − [n(O)]2 + 1

(i) X − (X ∪ Y )

(g) [n(P (L))]2 + n(O) + n(L − O)

(j) Y − (X ∩ Y )

(h) n(L∪O)+n(L∩O)+n(L−O)+[n(L−O)]3

(k) (X ∪ Y ) ∪ (X ∪ X)

(i) n[L − (O ∪ L)] + n[O ∪ (L ∩ O)] + [n(O)]2 2

22. Sea A = {1; 2; 3}, B = {2; 3} y C = {2; 3; 5}. Encontrar:

25. Sean los conjuntos: J = { 21 ; 45 ; − 21 ; − 45 },

(a) A ∪ B ∪ C

I = { 54 ; − 12 ; 59 ; 57 }, y

(b) A ∩ B ∩ C (c) (A ∪ C) ∩ B

L = {− 21 ; 25 ; − 52 }.

(d) (A − B) ∪ (B − C)

Encontrar:

(e) (A ∪ B) ∩ (B − C) ∪ (A − C) (f) A ∪ (B ∩ C) − (A ∩ B ∩ C)

(a) [n(J) + n(L) + n(I)]3

(g) P (A) ∩ P (B) ∩ P (C)

(b) n[P (I)] + n(L) + n[P (J)]

(h) P (A ∪ B ∪ C)

(c) n(L ∩ I ∩ J)

(i) n(A ∩ B ∩ C) + n(A ∪ B ∪ C)

(d) n[(L ∩ J) − (I ∪ L)]

(j) n(A − C) + n(B − C) + n(A − B)

(e) n[(L − J) ∩ (I − L)] (f) n[L ∪ (I − J)] + n[P (I)] + n(I)

23. Sean los conjuntos X = {x ∈ N : 1 < x < 4}, Y = {x ∈ N : 1 ≤ x ≤ 3}, y Z = {x ∈ N : 1 ≤ x < 5}. Encontrar:

(g) [n(L ∪ I)]2 + n(L − J) (h) n(L − J) + n(J − L) + n(I − L) + n(I − J) (i) n(I ∪ L) + n(J ∩ L) + n(J ∩ I) 26. Sean los conjuntos:

(a) n(X) + n(Y ) + n(Z)

√ √ √ D = { 2; − 2; 3},

(b) n[P (X)] + n[P (Y )] + n[P (Z)] (c) X ∪ Y ∪ Z

√ √ √ E = {− 2; 3; − 3} y

(d) X ∪ (Z − Y )

√ √ F={- 2; 3}.

(e) (X − Y ) ∩ (Y − Z) (f) Z ∪ X ∪ Y

Encontrar:

(g) (X ∩ Y ) ∪ (Z ∩ X) ∩ (Y ∪ Z)

(a) n(D − F ) + n(E − F ) + n(E − D)

(h) (X ∪ Y ∪ Z) − (X ∩ Y )

(b) n(D ∩ E ∩ F ) + n[P (F )]

24. Sean los conjuntos S = {−1; 0; 1; 2}, Q = {−2; −1; 0} y K = {−1; 1, 2}. Encontrar:

(c) n(E ∩ F ) + n(F ∩ D) + n(E ∪ F ) (d) n[F ∪ (E ∩ D)] (e) n[P (E)] + n(F ∪ D) + n(E ∩ D)

(a) [n(S) + n(Q) + n(K)]2

(f) n[(E − F ) ∪ (F − D)]

(b) n[P (Q)] + n[P (S)] + n[P (K)]

(g) [n(E ∪ D)]2 + [n(F − E)]2

(c) n(S ∩ Q ∩ K)

(h) n[P (E)] + [n(F ∪ D)]2

(d) n(S ∩ Q ∩ K) + n(S ∪ Q ∪ K)

(i) [n(E ∩ F )]3 + [n(E ∪ F )]3

(e) n(S − Q) + n(K − S) + n(Q − S)

(j) [n(E − D)]4 + [n(F − D)]3 + [n(D − E)]2

(f) n[S ∩ (K ∪ Q)] + n[P (S)] + n[P (S ∩ Q ∩ K)]

(k) [n(F ∪ D)]2 + n[P (E)] + n(E)

(g) n(S ∩ Q ∩ K) + n(S − Q) + n(K − Q) 3