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Mathematical Reasoning

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  1. 1.Choose the correct statement about two circles whose equations are given below.
  2. 2.Choose the incorrect statement about the two circles whose equations are given below: [x^2…
  3. 3.Statement 1: The only circle having radius √10 and a diameter along the line 2x+y=5 is x^2…
  4. 4.Which of the following statements is a tautology?
  5. 5.The statement [[p ((p q))]] is equivalent to :
  6. 6.Statement-1 : [ ( p q )] is equivalent to [p q].
  7. 7.Let S be a non-empty subset of R.
  8. 8.Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is ho…
  9. 9.The negation of the statement ``If I become a teacher, then I will open a school'' is :
  10. 10.Consider : Statement - I : [( p q ) ( p q )] is a fallacy.
  11. 11.The statement [( p ( q ) ) ( p ( q ) )] is
  12. 12.The negation of [ s ( r s )] is equivalent to :
  13. 13.The Boolean expression ((p [ ] q) [ ] (p [ ] [ ] q)) [ ] ([ ] p [ ] [ ] q) is equivalent t…
  14. 14.The contrapositive of the following statement, ``If the side of a square doubles, then its…
  15. 15.Consider the following two statements : P : If 7 is an odd number, then 7 is divisible by …
  16. 16.The following statement [( p q ) [ ( p q ) q ]] is :
  17. 17.The proposition [( p ) ( p q )] is equivalent to :
  18. 18.Contrapositive of the statement `If two numbers are not equal, then their squares are not …
  19. 19.The Boolean expression [ ( p q ) ( p q )] is equvalent to :
  20. 20.Consider the following two statements : Statement p : The value of sin 120o can be derived…
  21. 21.If (p [ ] [ ] q) [ ] (p [ ] r) [ ] [ ] p [ ] q is false, then the truth values of p, q and…
  22. 22.If p [ ] ([ ] p[ ] [ ] q) is false, then the truth values of p and q are respectively :
  23. 23.The negation of the Boolean expression ~ s [ ] (~r [ ] s) is equivalent to :
  24. 24.Which one of the following Boolean expressions is a tautology?
  25. 25.Consider the statement : "P(n) : n2 -- n + 41 is prime".
  26. 26.If q is false and p [ ] q [ ] r is true, then which one of the following statements is a t…
  27. 27.If the truth value of the statement p [ ] (~q [ ] r) is false (F), then the truth values o…
  28. 28.Which one of the following statements is not a tautology?
  29. 29.The contrapositive of the statement "If you are born in India, then you are a citizen of I…
  30. 30.If p [ ] (q [ ] r) is false, then the truth values of p, q, r are respectively :-
  31. 31.For any two statements p and q, the negation of the expression p [ ] (~p [ ] q) is :
  32. 32.If the Boolean expression (p [ ] q) [] (~ p [ ] q) is equivalent to p [] q, where [ , , ],…
  33. 33.Which of the following is a tautology ?
  34. 34.The contrapositive of the statement "If I reach the station in time, then I will catch the…
  35. 35.Let p, q, r be three statements such that the truth value of (p [ ] q) [ ] ([ ]q [ ] r) is…
  36. 36.Contrapositive of the statement : `If a function f is differentiable at a, then it is also…
  37. 37.Given the following two statements: [( S_1 ):( q p ) ( p q )] is a tautology [( S_2 ): ,, …
  38. 38.The negation of the Boolean expression x [ ] ~ y is equivalent to :
  39. 39.Consider the statement : ``For an integer n, if n3 -- 1 is even, then n is odd.'' The cont…
  40. 40.The negation of the Boolean expression p [ ] (~p [ ] q) is equivalent to :
  41. 41.Let A, B, C and D be four non-empty sets.
  42. 42.The logical statement (p [ ] q) [ ] ( q [ ] ~p) is equivalent to :
  43. 43.Which one of the following is a tautology?
  44. 44.Negation of the statement : [ 5 ] is an integer or 5 is an irrational is :
  45. 45.Which of the following Boolean expression is a tautology?
  46. 46.If the Boolean expression [(p q) (p q)] is a tautology, then [ ] and [ ] are respectively …
  47. 47.If the Boolean expression (p [ ] q) [ ] (q * ([ ]p) is a tautology, then the boolean expre…
  48. 48.If P and Q are two statements, then which of the following compound statement is a tautolo…
  49. 49.Which of the following is equivalent to the Boolean expression p [] [] q ?
  50. 50.Consider the following three statements : (A) If 3 + 3 = 7 then 4 + 3 = 8 (B) If 5 + 3 = 8…