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

### 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

### Question

The logical statement p ∧ q means ________.

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

### 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.

### 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

### 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

### Question

( p ∨ ∼p ) is the ________.

2. Conjunction
3. Tautology
4. Contingency

### Question

The converse of the conditional statement p → q is

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

### 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

### 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.

### Question

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

1. True
2. False

### Question

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

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

### Question

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

1. True
2. False

### 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

### Question

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

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

### 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.

### 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.

### Question

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

1. True
2. False

### Question

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

1. True
2. False

### 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

### Question

The switches in parallel act just like ________.

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

### 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.

### 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

### Question

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

1. True
2. False

### 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

### 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}

### 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)}

### 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

### 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.

### 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

### 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

### 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)}

### 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

### 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

### 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

### 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

### 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

### 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

### Question

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

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

### 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))

### 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

### 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

### Question

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

1. TRUE
2. FALSE

### 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

### 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

### 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

### Question

The set Z of all integers is _____.

1. uncountable
2. countable

### 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

### 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

### 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

### Question

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

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