1. A _______ is an ordered collection of objects. proposition relation set function 2. Among the integers 1 to 300, the number of integers which are divisible by 3 or 5 is 120 100 130 140 3. If p ?q is F, then p is f, q is f p is t, q is f p is t, q is t p is f, q is t 4. Which of the following is declarative statement? three is divisible by 3. i love you two may not be an even integer its right 5. If A = { (1, 2, 3}, then the relation R = {(2, 3)} in A is transitive only symmetric and transitive only not transitive symmetric only 6. The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ____________. 1010100000 1111111100 1010101101 1111101010 7. The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set ___________. {1, 6} {1, 2} {2, 5} {5, 6} 8. he set of positive integers is _________ . infinite subset empty finite 9. Let X be a family of sets and R be a relation in X, defined by A is disjoint from B. Then, R is transitive reflexive anti-symmetric symmetric 10. If (~ (p ? q)) ? q is F, then p is f, q is t p is t, q is t p is t, q is f p is f, q is 11. Which of the proposition is p ^ (~p v q) is logically equivalent to p ^ q contradiction tautulogy All of the options 12. If (~ p ? r) ^ (p ? q) is T and r is F, then truth values of p and q are: p is f, q is f p is f, q is t p is t, q is t p is t, q is f 13. If p ^ q is T, then p is t, q is t p is f, q is t p is f, q is f p is t, q is f 14. Two sets are called disjoint if there _____________ is the empty set. intersection complement difference union complement 15. If ((p ? q ) ? q) ? p is F, then p is t, q is t p is t, q is f p is f, q is f p is f, q is t 16. The set difference of the set A with null set is ________. U A B null 17. R is a relation defined in Z by aRb if and only if ab ³ 0, then R is symmetric transitive reflexive equivalence 18. Let P: I am in Bangalore.; Q: I love cricket.; then q -> p(q implies p) is? i am not in bangalore i love cricket if i love cricket then i am in bangalore if i am in bangalore then i love cricket 19. The premises (p ? q) ? r and r ? s imply which of the conclusion? q ? r p ? r p ? q p ? s 20. Let P (x) denote the statement x >7. Which of these have truth value true? p (4) p (0) p (6) p (9) 21. In proving v5 as irrational, we begin with assumption v5 is rational in which type of proof? mathematical induction vacuous proof direct proof proof by contradiction 22. Parul is out for a trip or it is not snowing and It is snowing or Raju is playing chess imply that parul is out for a trip and raju is playing chess raju is playing chess parul is out for a trip or raju is playing chess parul is out for trip 23. Let R be the set of real numbers. If f : R ? R is a function defined by f ( x ) = x2 , then f is] bijective subjective but not injective inject ve but not subjective None of the options 24. A proof covering all the possible cases, such type of proofs are known as proof by contradiction exhaustive proof vacuous proof direct proof 25. Translate ?x?y(x < y) in English, considering domain as a real number for both the variable. for all real number x there exists a real number y such that x is less than y for some real number x there exists a real number y such that x is less than y for each and every real number x and y such that x is less than y for every real number y there exists a real number x such that x is less than y 26. Let P: I am in Delhi.; Q: Delhi is clean.; then q ^ p(q and p) is? i am in delhi and delhi is not clean delhi is clean and i am in delhi delhi is not clean or i am in delhi delhi is clean but i am in mumbai 27. When to proof P?Q true, we proof P false, that type of proof is known as contrapositive proofs direct proof vacuous proof mathematical induction 28. Everyone wants to learn cosmology. This argument may be true for which domains? dall students in your cosmology class all the cosmology learning students in the world both all the cosmology learning students in the world and all students in your cosmology class None of the options 29. Which of the following can only be used in disproving the statements? counter example mathematical induction contrapositive proofs direct proof 30. Which of the following statement is a proposition? get me a glass of milkshake the only odd prime number is 2 what is the time now? god bless you! 31. A polygon with 7 sides can be triangulated into 10 14 7 5 32. A proof that p ? q is true based on the fact that q is true, such proofs are known as proof by cases trivial proof contrapositive proofs direct proof 33. Find the value of a4 for the recurrence relation an=2an-1+3, with a0=6. 221 141 65 320 34. In the principle of mathematical induction, which of the following steps is mandatory? inductive reference induction hypothesis induction set assumption minimal set representation 35. Find the number of factors of the product 58 * 75 * 23 which are perfect squares. 30 47 65 19 36. Determine the value of a2 for the recurrence relation an = 17an-1 + 30n with a0=3. 1437 5484 238 4387 37. For m = 1, 2,__, 4m+2 is a multiple of is known as conjecture lemma corollary None of the options 38. A polygon with 12 sides can be triangulated into 5 7 10 12 39. The number of diagonals can be drawn in a hexagon is 16 9 21 32 40. Which amount of postage can be formed using just 4-cent and 11-cent stamps? 2 30 5 10 41. For any integer m>=3, the series 2+4+6+_ +(4m) can be equivalent to mm m2+3 3m2+4 m+1 42. A non empty set A is termed as an algebraic structure with respect to ternary operation ? with respect to binary operation + with respect to binary operation * with respect to unary operation - 43. Matrix multiplication is a/an property. disjunctive commutative additive associative 44. What is multiplication of the sequence 1, 2, 3, 4,__ by the sequence 1, 3, 5, 7, 11,__? 4, 8, 9, 14, 28,_ 2, 8, 16, 35,_ 1, 4, 7, 9, 13,_ 1, 5, 14, 30,__ 45. If (M, *) is a cyclic group of order 73, then number of generator of G is equal to 23 17 89 72 46. A cyclic group is always monoid abelian group semigroup subgroup 47. What will be the sequence generated by the generating function 4x/(1-x)2? 0, 1, 1, 3, 5, 8, 13,_ 12, 16, 20, 24,_ 1, 3, 5, 7, 9,_ 0, 4, 8, 12, 16, 20,_ 48. A relation (34 x 78) x 57 = 57 x (78 x 34) can have property. closure distributive associative commutative 49. 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