Ejemplos En El Programa Latex

A L TEX ALUMNOS: MARTINEZ PUESCAS ANGELICA CURSO: MATEMATICA BASICA
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Dado los conjuntos : A = {5, 6, 7, 8} (1) B = {6, 1, 2, 7} (2) C = {5, 4, 7, 9} (3) U = {1, 2, 3, 4, 5, 6, 7, 8, 9} (4) Calcular : (5) 1. − A ∪ B (6) {5, 6, 8, 1, 2, 7} (7) 2. − (A ∩ B) ∪ C (8) {6, 7} ∪ {5, 4, 7, 9} (9) {6, 7, 5, 4, 9} (10) 3. − A ∩ (B − C) (11) {5, 6, 7, 8} ∩ {6, 1, 2} (12) {6} (13) 4. − C − (A ∩ B) (14){5, 4, 7, 9} − {5, 8, 1, 2, 4, 9, 3} (15) {7} (16)

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Dado los conjuntos : A = {1, 2, 3, 4} (17) B = {2, 3, 5, 7} (18) C = {1, 4, 6, 8} (19) U = {X ∈ N x ≤ 8} (20) U = {0, 1, 2, 3, 4, 5, 6, 7, 8} (21) calcular : (22) 5. − A ∪ B = {1, 2, 3, 4, 5, 7} (23) 6. − A ∩ B = {2, 3} (24) 7. − (A ∪ B) ∩ C (25) {1, 2, 3, 4, 5, 7} ∩ {1, 4, 6, 8} (26) {1, 4, 6, } (27) 8. − (A − B) respecto, aU (28) {0,2, 3, 5, 6, 7, 8} (29) 9. − C − (A ∪ B) respecto, aU (30) {1, 4, 6, 8} − {1, 2, 3, 4, 5, 7} (31) {8} (32) {0, 1, 2, 3, 4, 5, 6, 7} (33) (34)

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Si: A = {{1, 2, 3}3, 1} B = {1, 2, 3} C = {2, 3, 4} D = {{2, 3}1, 2, 5} 10. − A ∪ B {{1, 2, 3}1, 2, 3} 11. − A ∪ C {{1, 2, 3}1, 2, 3, 4} 12. − A ∪ D {{1, 2, 3}3{2, 3}1, 2, 5} 13. − A ∩ B {3, 1} 14. − A ∩ C {3} 15. − A ∩ D {1} 16. − A − B {{1, 2, 3}}A−C {{1, 2, 3}1} 17. − A − D {{1, 2, 3}3} (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (56) (57)

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Si: A = {x ∈ Z/xesdivisorde60} (58) A = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60} (59) B = {x ∈ Z/xesdivisorde42} (60) B = {1, 2, 3, 6, 7, 21, 42} (61) C = {x ∈ Z + /xesmultiplode2, menorque20} (62) C = {2, 4, 6, 8, 10, 12, 14, 18} (63)18. − A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (64) (A ∪ B) ∩ (A ∪ C) = (A ∪ B) ∩ (A ∪ C) (65) (A ∪ B) ∩ (A ∪ C) = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60} (66) 19. − A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (67) (A ∩ B) ∪ (A ∩ C) = (A ∩ B) ∪ (A ∩ C) (68) (A ∩ B) ∪ (A ∩ C) = {1, 2, 3, 4, 5, 6, 10, 12} (69) (70)

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20.-Sea: (71) U = {x ∈ N/x ≤ 7} (72) A = {x ∈ U/x ≤ 8} (73) B = {x ∈ U/xESmultiplode3} (74) C= {x ∈ U/x.x ≤ 25} (75) D = {x ∈ U/xespar} (76) Hallar : B − [(C ∪ D ) − A] (77) U = {1, 2, 3, 4, 5, 6} (78) A = {1, 2} (79) B = {3, 6} (80) C = {1, 4, 9, 16} (81) D = {2, 4, 6} (82) =⇒ {1, 2, 4, 5, 9, 16} − [{1, 2, 3, 5, 9, 16} − {1, 2}] (83) {1, 2, 4, 5, 9, 16} − {1, 2, 4} (84) {5, 9, 16} (85) (86)
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Sean: 21. − [2, 7 > [2, 7 > (88) 22.− < 1, 4 > < 1, 4 > (< 2, 6 > ∪ < 0, 1 > (89) <0, 1 > (90) < 0 > ∪ < 2, 4 > (91) 23. − [2, 9] ∩ (C < − ∝, −3] ∪ [3, 6])− < 2, 8] (92) [2, 9] ∩ ([−3, + ∝> − < 2, 8]) (93) [2, 9] ∩ [−3, 2 > ∪[8, + ∝> (94) < 2, + ∝> (95) 24. − (< − ∝, 5 > ∪ < 6, 12 >) < − ∝, 12] [1, 7] (97) < − ∝, 1] ∪ [7, 12] (98) (99) En las siguientes proposiciones dadas indicar cuales son verdaderas o falsas y [1, 7] (96) < 0, 1 > (87)

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justificar su respuestas: 25. −{x, y, z} = {z, x, y}(V ) (100) 26. − {x, x, x} = {x}(V ) (101) 27. − { {= { }(F ) (102) 28. − {{x, y}} ⊂ {z, {x, y}, w}(V ) (103) 29. − {x, y} ∈ {x, {x, y}}(V ) (104) 30. − {x, y} ⊂ {x, {x, y}}(V ) (105) 31. − {x, y} ⊂ {z, {x, y}, y}(V ) (106) 32. − {x, y} ⊂ {z, {x, y}, w}(V ) (107) 33. − {x, y, z} = {x, y, z}(F ) (108) 34. − a ⊂ { }(V ) (109) 35. − {a} ⊂ {{a}}(F ) (110) 36. − {a} ∈ {{a}}(V )(111) (112)

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37.-Simplificar las siguientes proposiciones a)A ∩ =A (113) b)A ∩ U = A (114) c)A ∪ A = U (115) d)A − e)A ∪ =A (116) =A (117) f )A ∪ U = U (118) g)A ∩ A = (119) h)(A ) = A (120) i)(A ∩ U ) = A (121) j)(A ∩ ) = A (122) k)(A ∪ ) = A (123) l)(A ∪ U ) = A (124) (125) 38.-Sea: A = { , 1, {1}} (126) HallarP (A) (127) 2 =8 (128) (129)
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39.-Sea: (130) A = { , 1, {1}} (131)HallarP (A), P (P (A)) (132) P (A) = 2 = 8 (133) P (P (A)) = 2 = 256 (134) (135)
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40.-Si: A = {1, 2, 3} (136) B = {x ∈ Z/x − x − 6 = 0} (137) C = {x ∈ N/2 < x < 6} (138) D = C − (A ∩ B) (139) Hallar : P (P (A)) (140) enB : F actorizamos (141) x −x−6 (142) x x −3 (143) −2 (144) (x − 2)(x − 3) = 0 (145) x = 2, 3 (146) B = {2, 3} (147) C = {3, 4, 5} (148) ⇒ D = {3, 4, 5} − {2, 3} (149) D...