In the name of ALLAH, the most beneficient, the most merciful

Discrete Mathematics (MTH202)

Multiple Choice Questions (MCQs)

 

Objective Questions

Question

The conjunction p ∧ q is True when _________.

  1. p is True, q is False
  2. p is False, q is True
  3. p is True, q is True
  4. p is False, q is False

Answer: 3 Chapter No. 1 

Question

The disjunction of p and q is written as ________.

  1. p ∨ q
  2. p ∧ q
  3. p XOR q
  4. None of the given

Answer: 1 Chapter No. 1 

Question

The logical statement p ∧ q means ________.

  1. p OR q
  2. p NOT q
  3. p AND q
  4. p XOR q

Answer: 3 Chapter No. 1 

Question

The disjunction p ∨ q is False when ________.

  1. p is False, q is True.
  2. p is True, q is False.
  3. p is True, q is True.
  4. p is False, q is False.

Answer: 4 Chapter No. 1 

Question

If p = It is raining, q = She will go to college
"It is raining and she will not go to college”
will be denoted by

  1. p ∧ ∼q
  2. p ∧ q
  3. ∼(p ∧ q)
  4. ∼p ∧ q

Answer: 1 Chapter No. 1 

Question

The negation of “Today is Friday” is

  1. Today is Saturday
  2. Today is not Friday
  3. Today is Thursday
  4. None of the given

Answer: 2 Chapter No. 1 

Question

( p ∨ ∼p ) is the ________.

  1. Contradiction
  2. Conjunction
  3. Tautology
  4. Contingency

Answer: 3 Chapter No. 2 

Question

The converse of the conditional statement p → q is

  1. q → p
  2. ∼q → ∼p
  3. ∼p → ∼q
  4. None of the given

Answer: 1 Chapter No. 3 

Question

Let p be True and q be True, then ( ∼p ∧ q ) is ________.

  1. t ( where t is tautology. )
  2. c ( where c is contradiction. )
  3. True
  4. False

Answer: 4 Chapter No. 3 

Question

The contrapositive of the conditional statement 'If it is Sunday, then I go for shopping' is ________.

  1. I do Not go for shopping, then it is Not Sunday.
  2. I go for shopping, then it is Sunday.
  3. I do Not go for shopping, then it is Sunday.
  4. I go for shopping, then it is Not Sunday.

Answer: 1 Chapter No. 3 

Question

The statement p → q is logically equivalent to ∼q → ∼p

  1. True
  2. False

Answer: 1 Chapter No. 3 

Question

Let p → q be a conditional statement, then the statement q → p is called ________.

  1. Inverse
  2. Converse
  3. Contrapositive
  4. Double conditional

Answer: 2 Chapter No. 3 

Question

If p is false and q is false, then ∼p implies q is ________.

  1. True
  2. False

Answer: 2 Chapter No. 3 

Question

The converse of the conditional statement 'If I live in Quetta, then I live in Pakistan' is ________.

  1. If I live in Pakistan, then I live in Quetta.
  2. If I live in Pakistan, then I do Not live in Quetta.
  3. If I do Not live in Quetta, then I do Not live in Pakistan
  4. If I do Not live in Quetta, then I live in Pakistan

Answer: 1 Chapter No. 3 

Question

∼(P → q) is logically equivalent to _________.

  1. p ∧ ∼q
  2. p ∨ ∼q
  3. ∼p ∧ q
  4. ∼p ∨ q

Answer: 1 Chapter No. 3 

Question

If p ↔ q is True, then ________.

  1. Only p is True.
  2. Only q is True.
  3. p and q both are True.
  4. None of the given.

Answer: 3 Chapter No. 4 

Question

'p is equivalent to q' means ________.

  1. p is not necessary but p is sufficient for q.
  2. p is neither necessary nor sufficient for q.
  3. p is necessary and sufficient for q.
  4. p is necessary but not sufficient for q.

Answer: 3 Chapter No. 4 

Question

What is the truth value of the sentence?
'It rains if and only if there are clouds.'

  1. True
  2. False

Answer: 2 Chapter No. 4 

Question

If p is false and q is true, then ∼p ↔ q is ________.

  1. True
  2. False

Answer: 1 Chapter No. 4 

Question

Let p1, p2, p3 be True premises in a given Truth Table. If the conjunctions of the Conclusion with each of p1, p2, p3 are True, then the argument is ________.

  1. False
  2. True
  3. Invalid
  4. Valid

Answer: 4 Chapter No. 5 

Question

The switches in parallel act just like ________.

  1. NOT gate
  2. AND gate
  3. OR gate
  4. XOR gate

Answer: 3 Chapter No. 5 

Question

Let A = {2, 3, 5, 7}, B = {2, 3, 5, 7, 2}, C = Set of first five prime numbers. Then from the following which statement is true ?

  1. A = B
  2. A = C
  3. B = C
  4. All the three sets are equal.

Answer: 1 Chapter No. 7 

Question

If A = Set of students of virtual university then A has been written in the _________.

  1. Tabular form
  2. Set builder form
  3. Descriptive form
  4. A is not a set

Answer: 3 Chapter No. 7 

Question

If A and B are any two sets, then A − B = B − A

  1. True
  2. False

Answer: 2 Chapter No. 8 

Question

x belongs to A or x belongs to B, therefore x belongs to ________.

  1. A intersection B
  2. A union B
  3. A difference B
  4. A symmetric difference B

Answer: 2 Chapter No. 8 

Question

Range of the relation {(0,1), (3,22), (90,34)} is __________ .

  1. {0, 3, 90}
  2. {1, 22, 34}
  3. {0, 1, 3}
  4. {0, 1, 3, 22, 90, 34}

Answer: 2 Chapter No. 11 

Question

Which of the followings is the product set A * B * C ? where A = {a}, B = {b}, and C = {c, d}.

  1. {(a, b, c), (a, b, d)}
  2. {(a, c, b), (a, d, b)}
  3. {(b, c, a), (b, d, a)}
  4. {(c, b, a), (d, b, a)}

Answer: 1 Chapter No. 11 

Question

Determine values of x and y, where (2x, x + y) = (8, 6).

  1. x = 3 and y = 5
  2. x = 4 and y = 2
  3. x = 6 and y = 12
  4. x = 4 and y = 12

Answer: 2 Chapter No. 11 

Question

Let R be the universal relation on a set A then which one of the following statement about R is true?

  1. R is not symmetric
  2. R is not reflexive
  3. R is not transitive
  4. R is reflexive, symmetric and transitive.

Answer: 4 Chapter No. 12 

Question

Let R be a relation on a set A. If R is symmetric then its compliment is __________.

  1. Reflexive
  2. Irreflexive
  3. Symmetric
  4. Antisymmetric

Answer: 2 Chapter No. 14 

Question

Let R be a relation on a set A. If R is reflexive then its compliment is ____________.

  1. Reflexive
  2. Irreflexive
  3. Symmetric
  4. Antisymmetric

Answer: 2 Chapter No. 14 

Question

R = {(a,1), (b,2), (c,3), (d,4)} then the inverse of this relation is _______.

  1. {(a,1), (b,2), (3,c), (4,d)}
  2. {(1,a), (2,b), (3,c), (4,d)}
  3. {(a,1), (2,b), (3,c), (4,d)}
  4. {(1,a), (b,2), (3,c), (4,d)}

Answer: 2 Chapter No. 14 

Question

Let R be a relation on a set A. If R is reflexive then its compliment is ________ .

  1. Reflexive
  2. Irreflexive
  3. Symmetric
  4. Antisymmetric

Answer: 2 Chapter No. 14 

Question

Which relations below are functions?
R1 = {(3,4), (4,5), (6,7), (8,9)}
R2 = {(3,4), (4,5), (6,7), (3,9)}
R3 = {(-3,4), (4,-5), (0,0), (8,9)}
R4 = {(8,11), (34,5), (6,17), (8,19)}

  1. R1 and R3 are functions
  2. R1 and R2 are functions
  3. R2 and R4 are functions
  4. R3 and R2 are functions

Answer: 1 Chapter No. 15 

Question

For the following relation to be a function, x can not be what values?
R = {(2,4), (x,1), (4,2), (5,6)}

  1. x cannot be 2, 4 or 5
  2. x cannot be 4, 1 or 6
  3. x cannot be 2, 4 or 6
  4. x cannot be 1, 2 or 6

Answer: 1 Chapter No. 15 

Question

Let X = {2, 4, 5} and Y= {1, 2, 4} and R be a relation from X to Y defined by R = {(2,4), (4,1), (a,2)}. For what value of ‘a‘ the relation R is a function ?

  1. 1
  2. 2
  3. 4
  4. 5

Answer: 4 Chapter No. 15 

Question

Let A = {1, 2, 3} and B = {2, 4} then number of functions from A to B are _________.

  1. 6
  2. 8
  3. 16
  4. 64

Answer: 2 Chapter No. 15 

Question

Let A = {1, 2, 3, 4} and B = {7} then the constant function from A to B is _________ .

  1. Onto
  2. One to one
  3. Both one to one and onto
  4. Neither one to one nor onto

Answer: 1 Chapter No. 16 

Question

One-to-One correspondence means the condition of ______.

  1. one-One
  2. identity
  3. onto
  4. one-One and onto

Answer: 4 Chapter No. 16 

Question

If a function (g o f)(x):X→Z is defined as (g o f)(x) = g(f(x)) for all x ∈ X. Then the function ________ is known as composition of f and g.

  1. (f o g)
  2. f-1(g(x))
  3. (g o f)
  4. g-1(f(x))

Answer: 3 Chapter No. 17 

Question

Let g be a function defined by g(x) = x + 1. Then the composition of (g o g)(x)is ______.

  1. x
  2. x + 1
  3. x + 2
  4. x2 + 2x + 1

Answer: 3 Chapter No. 17 

Question

The functions 'f' and 'g' are inverse of each other if and only if their composition gives _______.

  1. constant function
  2. identity function
  3. bijective function
  4. injective function

Answer: 2 Chapter No. 17 

Question

The functions f o g and g o f are always equal.

  1. TRUE
  2. FALSE

Answer: 2 Chapter No. 17 

Question

A set is called finite, if and only if, it is the ________ or there is ________ .

  1. empty set, onto
  2. empty set, one-to-one
  3. one-to-one, onto
  4. empty set, bijective

Answer: 2 Chapter No. 18 

Question

If f and g are two one-to-one functions, then their composition that is gof is one-to-one.

  1. TRUE
  2. FALSE

Answer: 1 Chapter No. 18 

Question

Let f(x) = x2 + 1 define functions f from R to R and c = 2 be any scalar, then c.f(x) is ______.

  1. 2
  2. x2 + 1
  3. 2x2 - 1
  4. 2x2 + 2

Answer: 4 Chapter No. 18 

Question

The set Z of all integers is _____.

  1. uncountable
  2. countable

Answer: 2 Chapter No. 18 

Question

Let f(x) = 3x and g(x) = x + 2 define functions f and g from R to R, then (f.g)(x) is _____.

  1. 2x − 2
  2. 3x + 2
  3. 4x + 2
  4. 3x2 + 6x

Answer: 4 Chapter No. 18 

Question

Real valued function is a function that assigns _______ to each member of its domain.

  1. negative real number
  2. positive real number
  3. only a real number
  4. any arbitrary real number

Answer: 3 Chapter No. 18 

Question

Let f(x)=3x and g(x) = 3x − 2 define functions f and g from R to R. Then (f+g)(x) = ________.

  1. −2
  2. 6x + 2
  3. 6x − 2
  4. 6x.x − 2

Answer: 3 Chapter No. 18 

Question

The total number of terms in an arithmetic series 0 + 5 + 10 + 15 + .... + 50 are ________.

  1. 9
  2. 10
  3. 11
  4. infinite

Answer: 3 Chapter No. 20