# Discrete mathematics mcq pdf | DM mcq sppu

## DM mcq pdf pune university

40 most important DM mcq questions and answers are listed below. discrete mathematics mcq pdf is also given below that can help in study of dm mcq sppu online exam. dm mcq questions and answers pdf are also made available for free download.

Q. A _ is an ordered collection of objects.
A. Relation
B. Function
C. Set
D. Proposition

Set

Q. Power set of empty set has exactly _ subset.
A. One
B. Two
C. Zero
D. Three

One

Q. 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}

{1, 3, 5, 7, 9}

Q. What is the cardinality of the set of odd positive integers less than 10?
A. 10
B. 5
C. 3
D. 20

5

Q. 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}

A = {1, 2, 3} and B = {2, 1, 3}

Q. The set of positive integers is __.
A. Infinite
B. Finite
C. Subset
D. Empty

Infinite

Q. What is the Cardinality of the Power set of the set {0, 1, 2}.
A. 8
B. 6
C. 7
D. 9

8

## DM mcq pdf Pune University

Q. 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}

{0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

Q. 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}

{1, 2, 5, 6}

## DM mcq questions and answers pdf

Q. 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}

{1, 2}

Q. Two sets are called disjoint if there _ is the empty set.
A. Union Complement
B. Difference
C. Intersection
D. Complement

Intersection

Q. 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}

{1, 3, 5} and {2, 4, 6}

Q. The difference of {1, 2, 3} and {1, 2, 5} is the set _.
A. {1}
B. {5}
C. {3}
D. {2}

{3}

Q. The complement of the set A is _.
A. A – B
B. U – A
C. A – U
D. B – A

U – A

Q. The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is __.
A. 1010100000
B. 1010101101
C. 1111111100
D. 1111101010

1111101010

Q. The set difference of the set A with null set is __.
A. A
B. null
C. U
D. B

A

Q. 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}, ∅}

{a, b, ∅}

## DM mcq questions pdf

Q. 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

(A ∪ B) – C

Q. 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

140

Q. 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

43 = 13 + 15 + 17 + 19

Q. By mathematical Induction 2n>n3
A. for n ≥ 1
B. for n ≥ 4
C. for n ≥ 5
D. for n ≥ 10

for n ≥ 10

Q. 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)

(A ∪ B) – (A ∩ B)

Q. 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

A ⊕ B

Q. 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

A ∩ B’

Q. The number of subsets of a set containing n elements is
A. n
B. 2n-1
C. n2
D. 2n

2n

Q. What is the cardinality of the set of odd positive integers less than 10?
A. 10
B. 5
C. 3
D. 20

5

Q. 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}

A = {1, 2, 3} and B = {2, 1, 3}

Q. 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}

{1, 3, 5, 7, 9}

Q. Power set of empty set has exactly _ subset.
A. One
B. Two
C. Zero
D. Three

One

Q. The set of positive integers is _ .
A. Infinite
B. Finite
C. Subset
D. Empty

MCQs on Logic & Propositions

Infinite

Q. 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

p is F, q is T

Q. 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

p is T, q is F

Q. The statement from ∼ (p ˄ q) is logically equivalent to
A. ∼ p ˅ ∼ q
B. ∼ p ˅ qC
C. p ˅ ∼ q
D. ∼ p ˄∼ q

∼ p ˅ ∼ q

Q. p → p is logically equivalent to
A. p
B. Tautology
D. None of these

Tautology

Q. The converse of p → q is
A. ∼q → ∼p
B. ∼ p → ∼ q
C. ∼ p → q
D. q → p

q → p

Q. 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

p ˄ ∼ q

Q. 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

p → q

Q. 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

∼ p ˅ q

Q. 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

p is T, q is T

Q. 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

p is F, q is T

## DM mcq sppu

Q. 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

p is T, q is T

Q. 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

p is F, q is T

Q. (p ˄ (p → q )) → q is logically equivalent to
A. p ˅ q
B. (p ˄ q) ˅ (~ p˄ ~q)
C. Tautology
D. (~ p ˅ q) ˄ (p ˅ q)

Tautology

Q. 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

p and q must have same truth values

Q. 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)

(p ˄ ~q )→ r

2.Two of them are not true
3.The average increase in IQ scores of people who learn this game is more than 20 points.

Q. Which of the following statement is false?
A. (1)
B. (2)
C. (3)
D. None of these

(2)

Q. The contrapositive of p →q is
A. ~ q → ~ p
B. ~ p → ~ qC
C. ~ p → q
D. ~ q → p

~ q → ~ p

Q. 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

Three is divisible by 3.

Q. The following propositional statement is (P → (Q v R)) → ((P ^ Q) → R)
A. Satisfiable but not valid
B. valid
D. none of the above
p>

landscape

Q. Which of the proposition is p ^ (~p v q) is
A. Tautulogy
C. Logically equivalent to p ^ q
D. All of above

MCQs on Relations and Functions

Logically equivalent to p ^ q

Q. 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}

Range of R = {5}

Q. 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

None of the above

Q. 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

{– 2, – 1, 0, 1, 2}

Q. 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

not transitive

Q. 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

symmetric

Q. R is a relation defined in Z by aRb if and only if ab ³ 0, then R is
A. reflexive
B. symmetric
C. transitive
D. equivalence

equivalence

Q. Let a relation R in the set R of real numbers be defined as (a, b) Î R if and only if 1 + ab > 0 for all a, bÎR. The relation R is
A. Reflexive and Symmetric
B. Symmetric and Transitive
C. Only transitive
D. An equivalence relation

Reflexive and Symmetric

Q. If R be relation ‘<‘ from A = {1, 2, 3, 4} to B = {1, 3, 5} ie, (a, b) Î R iff a < b, then RoR– 1 is
A. {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
B. {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}
C. {(3, 3), (3, 5), (5, 3), (5, 5)}
D. { (3, 3), (3, 4), (4, 5)}

{(3, 3), (3, 5), (5, 3), (5, 5)}

Q. The range of the function when f(x)= X-2/2-x x ¹ 2 is
A. R
B. R – {1}
C. {– 1}
D. R – {– 1}

{– 1}

Q. R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R – 1 is
A. {(11, 8), (13, 10)}
B. {(8, 11), (10, 13)}
C. {(8, 11), (9, 12), (10, 13)}
D. None of the above

{(8, 11), (10, 13)}

Q. R is a relation on N given by N = {(x, y): 4x + 3y = 20}. Which of the following belongs to R?
A. (– 4, 12)
B. (5, 0)
C. (3, 4)
D. (2, 4)

(2, 4)

Q. The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3} is given
A. {(1, 4), (2, 5), (3, 6), ….}
B. { (4, 1), (5, 2), (6, 3), ….}
C. {(4, 1), (5, 2), (6, 3), ….}
D. None of the above

{ (4, 1), (5, 2), (6, 3), ….}

Q. Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is
A. 7
B. 9
C. 10
D. 12

7

Q. Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then, n (X ÇY) is equal to
A. 4
B. 6
C. 8
D. 12

12

Q. Let R = { ( 3, 3 ) ( 6, 6 ) ( ( 9, 9 ) ( 12, 12 ), ( 6, 12 ) ( 3, 9 ) ( 3, 12 ), ( 3, 6 ) } be a relation on the set A = { 3, 6, 9, 12 }. The relation is
A. reflexive and transitive
B. reflexive only
C. an equivalence relation
D. reflexive and symmetric only

reflexive and transitive

Q. Let f : ( – 1, 1 ) → B be a function defined by f ( x ) = 2 1 x 1 2x tan – – , then f is both one-one and onto when B is the interval
A. (0, 𝜋/2)
B. (0, −𝜋/2)
C. (𝜋/2,−𝜋/2)
D. (−𝜋/2,𝜋/2)

(−𝜋/2,𝜋/2)

Q. Let R be the set of real numbers. If f : R → R is a function defined by f ( x ) = x2, then f is]
A. inject ve but not subjective
B. subjective but not injective
C. bijective
D. none of these

none of these

Q. Domain of √(4x-x2 ) is
A. [0, 4]
B. (0, 4)
C. R ฀ (0, 4)
D. R ฀ [0, 4]

[0, 4]

Q. The domain of √[(x-2)(3-X)] is
A. (2, 3)
B. (2, 3]
C. [2, 3]
D. None of these.