**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

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**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}

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**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, ∅}

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**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. 4^{3}= 15 + 17 + 19 + 21

B. 4^{3}= 11 + 13 + 15 + 17 + 19

C. 4^{3} = 13 + 15 + 17 + 19

D. 4^{3} = 13 + 15 + 17 + 19 + 21

43 = 13 + 15 + 17 + 19

**Q. By mathematical Induction 2 ^{n}>n^{3}**

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. 2^{n}-1

C. n^{2}

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

C. Contradiction

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

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**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

**Q. Consider a following advertisement for a game:***1.There are three statements in this advertisement2.Two of them are not true3.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

C. a contadiction

D. none of the above

p>

landscape

**Q. Which of the proposition is p ^ (~p v q) is**

A. Tautulogy

B. Contradiction

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), ….}

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**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 ) = x ^{2}, 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-x**^{2}** ) 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.

[2, 3]

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