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Mathematical Reasoning

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  1. 51.Which of the following Boolean expressions is not a tautology?
  2. 52.The negation of the statement [ p (p q)] is :
  3. 53.For the statements p and q, consider the following compound statements : (a) [( q (p q)) p…
  4. 54.The statement among the following that is a tautology is :
  5. 55.The contrapositive of the statement "If you will work, you will earn money" is :
  6. 56.The statement [B ( ( A ) B )] is equivalent to :
  7. 57.Consider the statement "The match will be played only if the weather is good and ground is…
  8. 58.Consider the two statements : (S1) : (p [] q) [ ] ([ ] q [] p) is a tautology .
  9. 59.If the truth value of the Boolean expression [( ( p q ) ( q r ) ( r ) ) ( p q )] is false,…
  10. 60.Let F1(A, B, C) = (A [ ] [ ] B) [ ] [[]C [] (A [] B)] [] [] A and F2(A, B) = (A [] B) [] (…
  11. 61.The Boolean expression (p [] q) [] ((r [] q) [] p) is equivalent to :
  12. 62.The statement (p [ ] (p [] q) [] (q [] r)) [] r is :
  13. 63.Which of the following is the negation of the statement "for all M > 0, there exists x[]S …
  14. 64.The compound statement [( (P Q) ) ( ( P) Q ) ( ( P) ( Q) )] is equivalent to
  15. 65.Negation of the statement (p [] r) [] (q [] r) is :
  16. 66.Let *, [][], [] be such that the Boolean expression (p * [] q) [] (p q) is a tautology.
  17. 67.Consider the following statements: A : Rishi is a judge.
  18. 68.The number of choices for [ , , , ], such that [(p q) ((p q) (( p) q))] is a tautology, is…
  19. 69.Consider the following statements: P : Ramu is intelligent.
  20. 70.The negation of the Boolean expression (([] q) [] p) [] (([] p) [] q) is logically equival…
  21. 71.Consider the following two propositions: [P1: (p q)] [P2:(p q) (( p) q)] If the propositio…
  22. 72.Negation of the Boolean expression [p (q p)] is
  23. 73.Let r [] p, q, []p, []q be such that the logical statement r [] ([]p) [] (p [] q) [] r is …
  24. 74.Let [], [ ] [] [], [] be such that p [] q [] ((p [] q) [] r) is a tautology.
  25. 75.If the truth value of the statement [(P ( R)) (( R) Q)] is F, then the truth value of whic…
  26. 76.[(p r) (p ( q))] is equivalent to [( p)] when r is
  27. 77.Which of the following statement is a tautology?
  28. 78.Let [p] : Ramesh listens to music.
  29. 79.Let the operations [*, , ].
  30. 80.Let p, q, r be three logical statements.
  31. 81.The statement [(p q) (p r)] is NOT equivalent to
  32. 82.The statement [(p q) (p r)] is equivalent to :
  33. 83.Negation of the Boolean statement (p [] q) [] (([] r) [] p) is equivalent to :
  34. 84.Let [] [] [], [], [], [] be such that (p [] q) [] ((p [] q) [] q) is a tautology.
  35. 85.The conditional statement [((p q) (( p) r)) ((( p) r) (p q))] is :
  36. 86.The negation of the statement [(p q) (q ( r))] is :
  37. 87.The converse of [(( p) q) r] is
  38. 88.Among the two statements [(S 1):(p q) (p ( q))] is a contradiction and [(S 2):(p q) (( p) …
  39. 89.The statement [(p ( q)) (( p) q) (( p) ( q))] is equivalent to _________.
  40. 90.The negation of the statement [((A (B C)) (A B)) A] is
  41. 91.Negation of p (q (p q)) is :
  42. 92.The negation of the expression [q ( ( ,q) p )] is equivalent to
  43. 93.Let p and q be two statements.
  44. 94.Let [ , , ] be such that [(p q) (p q)] is a tautology.
  45. 95.If p,q and r are three propositions, then which of the following combination of truth valu…
  46. 96.Consider the following statements: P : I have fever Q: I will not take medicine R : I will…
  47. 97.Among the statements : [(S 1)~((p q) r) (p r)] [(S 2)~((p q) r) ((p r) (q r))]
  48. 98.The number of values of r p, q, p, q for which ((p q) (r q)) ((p r) q) is a tautology, is …
  49. 99.[(S 1)~(p q) (p ( q))] is a tautology [(S 2)~(( p) ( q)) (( p) q)] is a contradiction.
  50. 100.Among the statements (S1) : [(p q) (( p) q)] is a tautology (S2) : [(q p) (( p) q)] is a c…