McqMate
These multiplechoice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Computer Science Engineering (CSE) .
1. 
A _______ is an ordered collection of objects. 
A.  relation 
B.  function 
C.  set 
D.  proposition 
Answer» C. set 
2. 
Power set of empty set has exactly _____ subset. 
A.  one 
B.  two 
C.  zero 
D.  three 
Answer» A. one 
3. 
The set O of odd positive integers less than 10 can be expressed by ___________ 
A.  {1, 2, 3} 
B.  {1, 3, 5, 7, 9} 
C.  {1, 2, 5, 9} 
D.  {1, 5, 7, 9, 11} 
Answer» B. {1, 3, 5, 7, 9} 
4. 
What is the cardinality of the set of odd positive integers less than 10? 
A.  10 
B.  5 
C.  3 
D.  20 
Answer» B. 5 
5. 
Which of the following two sets are equal? 
A.  a = {1, 2} and b = {1} 
B.  a = {1, 2} and b = {1, 2, 3} 
C.  a = {1, 2, 3} and b = {2, 1, 3} 
D.  a = {1, 2, 4} and b = {1, 2, 3} 
Answer» C. a = {1, 2, 3} and b = {2, 1, 3} 
6. 
The set of positive integers is ________. 
A.  infinite 
B.  finite 
C.  subset 
D.  empty 
Answer» A. infinite 
7. 
What is the Cardinality of the Power set of the set {0, 1, 2}. 
A.  8 
B.  6 
C.  7 
D.  9 
Answer» A. 8 
8. 
The members of the set S = {x x is the square of an integer and x < 100} is _________________. 
A.  {0, 2, 4, 5, 9, 58, 49, 56, 99, 12} 
B.  {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} 
C.  {1, 4, 9, 16, 25, 36, 64, 81, 85, 99} 
D.  {0, 1, 4, 9, 16, 25, 36, 49, 64, 121} 
Answer» B. {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} 
9. 
The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________. 
A.  {1, 2, 6, 1} 
B.  {1, 2, 5, 6} 
C.  {1, 2, 1, 2} 
D.  {1, 5, 6, 3} 
Answer» B. {1, 2, 5, 6} 
10. 
The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set ___________. 
A.  {1, 2} 
B.  {5, 6} 
C.  {2, 5} 
D.  {1, 6} 
Answer» A. {1, 2} 
11. 
Two sets are called disjoint if there _____________ is the empty set. 
A.  union complement 
B.  difference 
C.  intersection 
D.  complement 
Answer» C. intersection 
12. 
Which of the following two sets are disjoint? 
A.  {1, 3, 5} and {1, 3, 6} 
B.  {1, 2, 3} and {1, 2, 3} 
C.  {1, 3, 5} and {2, 3, 4} 
D.  {1, 3, 5} and {2, 4, 6} 
Answer» D. {1, 3, 5} and {2, 4, 6} 
13. 
The difference of {1, 2, 3} and {1, 2, 5} is the set _________. 
A.  {1} 
B.  {5} 
C.  {3} 
D.  {2} 
Answer» C. {3} 
14. 
The complement of the set A is _____________. 
A.  a – b 
B.  u – a 
C.  a – u 
D.  b – a 
Answer» B. u – a 
15. 
The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ____________. 
A.  1010100000 
B.  1010101101 
C.  1111111100 
D.  1111101010 
Answer» D. 1111101010 
16. 
The set difference of the set A with null set is ________. 
A.  A 
B.  null 
C.  U 
D.  B 
Answer» A. A 
17. 
If A = {a,b,{a,c}, ∅}, then A  {a,c} is 
A.  {a, b, ∅} 
B.  {b, {a, c}, ∅} 
C.  {c, {b, c}} 
D.  {b, {a, c}, ∅} 
Answer» A. {a, b, ∅} 
18. 
The set (A  B) – C is equal to the set 
A.  (a – b) ∩ c 
B.  (a∪ b) – c 
C.  (a – b) ∪ c 
D.  (a ∪ b) – c 
Answer» D. (a ∪ b) – c 
19. 
Among the integers 1 to 300, the number of integers which are divisible by 3 or 5 is 
A.  100 
B.  120 
C.  130 
D.  140 
Answer» D. 140 
20. 
Using Induction Principle if 13 = 1, 23 = 3 + 5, 33 = 7 + 9 + 11, then 
A.  43= 15 + 17 + 19 + 21 
B.  43= 11 + 13 + 15 + 17 + 19 
C.  43 = 13 + 15 + 17 + 19 
D.  43 = 13 + 15 + 17 + 19 + 21 
Answer» C. 43 = 13 + 15 + 17 + 19 
21. 
By mathematical Induction 2n> n3 
A.  for n ≥ 1 
B.  for n ≥ 4 
C.  for n ≥ 5 
D.  for n ≥ 10 
Answer» D. for n ≥ 10 
22. 
The symmetric difference A ⊕ B is the set 
A.  a – a ∩ b 
B.  (a∪ b) – (a∩ b) 
C.  (a – b) ∩ (b – a) 
D.  a ∪ (b – a) 
Answer» B. (a∪ b) – (a∩ b) 
23. 
If A is the set of students who play crocket, B is the set of students who play football then the set of students who play either football or cricket, but not both, can be symbolically depicted as the set 
A.  a ⊕ b 
B.  a ∪ b 
C.  a – b 
D.  a ∩ b 
Answer» A. a ⊕ b 
24. 
Let A and B be two sets in the same universal set. Then A – B = 
A.  A ∩ B 
B.  A ∪ B 
C.  A ∩ B' 
D.  none of these 
Answer» C. A ∩ B' 
25. 
The number of subsets of a set containing n elements is 
A.  n 
B.  2n  1 
C.  n2 
D.  2n 
Answer» D. 2n 
26. 
The set O of odd positive integers less than 10 can be expressed by ___________ . 
A.  {1, 2, 3} 
B.  {1, 3, 5, 7, 9} 
C.  {1, 2, 5, 9} 
D.  {1, 5, 7, 9, 11} 
Answer» B. {1, 3, 5, 7, 9} 
27. 
he set of positive integers is _________ . 
A.  infinite 
B.  finite 
C.  subset 
D.  empty 
Answer» A. infinite 
28. 
If p ˄ q is T, then 
A.  p is t, q is t 
B.  p is f, q is t 
C.  p is f, q is f 
D.  p is t, q is f 
Answer» B. p is f, q is t 
29. 
If p →q is F, then 
A.  p is t, q is t 
B.  p is f, q is t 
C.  p is f, q is f 
D.  p is t, q is f 
Answer» D. p is t, q is f 
30. 
The statement from ∼ (p ˄ q) is logically equivalent to 
A.  ∼ p ˅ ∼ q 
B.  ∼ p ˅ qc 
C.  p ˅ ∼ q 
D.  ∼ p ˄∼ q 
Answer» A. ∼ p ˅ ∼ q 
31. 
p → p is logically equivalent to 
A.  p 
B.  tautology 
C.  contradiction 
D.  none of these 
Answer» B. tautology 
32. 
The converse of p → q is 
A.  ∼q → ∼p 
B.  ∼ p → ∼ q 
C.  ∼ p → q 
D.  q → p 
Answer» D. q → p 
33. 
Let p: Mohan is rich, q : Mohan is happy, then the statement: Mohan is rich, but Mohan is not happy in symbolic form is 
A.  p ˄ q 
B.  ∼ p˄ q 
C.  p ˅ q 
D.  p ˄ ∼ q 
Answer» D. p ˄ ∼ q 
34. 
Let p: I will get a job, q: I pass the exam, then the statement form: I will get a job only if I pass the exam, in symbolic from is 
A.  p → q 
B.  p ˄ q 
C.  q → p 
D.  p ˄ q 
Answer» A. p → q 
35. 
Let p denote the statement: “Gopal is tall”, q: “Gopal is handsome”. Then the negation of the statement Gopal is tall, but not handsome,in symbolic form is: 
A.  ∼ p ˄q 
B.  ∼ p ˅ q 
C.  ∼ p ˅∼q 
D.  ∼ p ˄∼q 
Answer» B. ∼ p ˅ q 
36. 
If p ˄ (p → q) is T, then 
A.  p is t 
B.  p is f, q is t 
C.  p is t, q is t 
D.  p is f, q is f 
Answer» C. p is t, q is t 
37. 
If (∼ (p ˅ q)) → q is F, then 
A.  p is t, q is f 
B.  p is f, q is t 
C.  p is t, q is t 
D.  p is f, q is 
Answer» B. p is f, q is t 
38. 
If (∼ p → r) ˄ (p ↔ q) is T and r is F, then truth values of p and q are: 
A.  p is t, q is t 
B.  p is t, q is f 
C.  p is f, q is f 
D.  p is f, q is t 
Answer» A. p is t, q is t 
39. 
If ((p → q ) → q) → p is F, then 
A.  p is t, q is t 
B.  p is t, q is f 
C.  p is f, q is t 
D.  p is f, q is f 
Answer» C. p is f, q is t 
40. 
(p ˄ (p → q )) → q is logically equivalent to 
A.  p ˅ q 
B.  (p ˄ q) ˅ (~ p˄ ~q) 
C.  tautology 
D.  (~ p ˅ q) ˄ (p ˅ q) 
Answer» C. tautology 
41. 
If (p ˅ q) ˄ (~ p˅ ~q) is F, then 
A.  p is t, q is t, or q is f 
B.  p is f, q is t 
C.  p is t, q is f 
D.  p and q must have same truth values 
Answer» D. p and q must have same truth values 
42. 
Let p denote the statement: “I finish my homework before dinner”, q: “It rains” and r: “I will go for a walk”, the representative of the following statement: if I finish my homework before dinner and it does not rain, then I will go for walk is 
A.  p ˄ ~q ˄ r 
B.  (p ˄ ~q )→ r 
C.  p →(~q˄ r) 
D.  (p →~q)→ r) 
Answer» B. (p ˄ ~q )→ r 
43. 
The contrapositive of p →q is 
A.  ~ q → ~ p 
B.  ~ p → ~ qc 
C.  ~ p → q 
D.  ~ q → p 
Answer» A. ~ q → ~ p 
44. 
Which of the following is declarative statement? 
A.  it’s right 
B.  three is divisible by 3. 
C.  two may not be an even integer 
D.  i love you 
Answer» B. three is divisible by 3. 
45. 
Which of the proposition is p ^ (~p v q) is 
A.  tautulogy 
B.  contradiction 
C.  logically equivalent to p ^ q 
D.  all of above 
Answer» C. logically equivalent to p ^ q 
46. 
The relation R defined in A = {1, 2, 3} by aRb, if

A.  r = {(1, 1), (2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)} 
B.  r–1 = r 
C.  domain of r = {1, 2, 3} 
D.  range of r = {5} 
Answer» D. range of r = {5} 
47. 
The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) :

A.  {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} 
B.  {(2, 2), (3, 2), (4, 2), (2, 4)} 
C.  {(3, 3), (4, 3), (5, 4), (3, 4)} 
D.  none of the above 
Answer» D. none of the above 
48. 
If R = {x, y) : x, y Î Z, x2 + y2 £ 4} is a relation in z, then domain of R is 
A.  {0, 1, 2} 
B.  {– 2, – 1, 0} 
C.  {– 2, – 1, 0, 1, 2} 
D.  none of these 
Answer» C. {– 2, – 1, 0, 1, 2} 
49. 
If A = { (1, 2, 3}, then the relation R = {(2, 3)} in A is 
A.  symmetric and transitive only 
B.  symmetric only 
C.  transitive only 
D.  not transitive 
Answer» D. not transitive 
50. 
Let X be a family of sets and R be a relation in X, defined by ‘A is disjoint from B’. Then, R is 
A.  reflexive 
B.  symmetric 
C.  antisymmetric 
D.  transitive 
Answer» B. symmetric 
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