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440+ Discrete Mathematics Solved MCQs

These multiple-choice 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
a2 – b2
£ 5. Which of the following is false?

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) :
x2 – y2
< 16} is given by

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. anti-symmetric
D. transitive
Answer» B. symmetric

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