## Objective Questions

*Question*

The conjunction p and q is True when _________.

- p is True, q is False
- p is False, q is True
- p is True, q is True
- p is False, q is False

Answer: 3 | Chapter No. 1 |

*Question*

The disjunction of p and q is written as ________.

- p v q
- p ^ q
- p XOR q
- None of the given

Answer: 1 | Chapter No. 1 |

*Question*

The logical statement p ^ q means ________.

- p OR q
- p Not q
- p AND q
- p XOR q

Answer: 3 | Chapter No. 1 |

*Question*

The disjunction p v q is False when ________.

- p is False, q is True.
- p is True, q is False.
- p is True, q is True.
- p is False, q is False.

Answer: 4 | Chapter No. 1 |

*Question*

( p v ~ p ) is the ________.

- Contradiction
- Conjunction
- Tautology
- Contingency

Answer: 3 | Chapter No. 2 |

*Question*

Let p be True and q be True, then ( ~ p AND q ) is ________.

- t ( where t is tautology. )
- c ( where c is contradiction. )
- True
- False

Answer: 4 | Chapter No. 3 |

*Question*

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

- I do Not go for shopping, then it is Not Sunday.
- I go for shopping, then it is Sunday.
- I do Not go for shopping, then it is Sunday.
- 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

- True
- False

Answer: 1 | Chapter No. 3 |

*Question*

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

- Inverse
- Converse
- Contrapositive
- Double conditional

Answer: 2 | Chapter No. 3 |

*Question*

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

- True
- False

Answer: 2 | Chapter No. 3 |

*Question*

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

- If I live in Pakistan, then I live in Quetta.
- If I live in Pakistan, then I do Not live in Quetta.
- If I do Not live in Quetta, then I do Not live in Pakistan
- If I do Not live in Quetta, then I live in Pakistan

Answer: 1 | Chapter No. 3 |

*Question*

~(P --> q) is logically equivalent to _________.

- p AND ~ q
- p OR ~q
- ~p AND q
- ~p OR q

Answer: 1 | Chapter No. 3 |

*Question*

If p <--> q is True, then ________.

- Only p is True.
- Only q is True.
- p and q both are True.
- None of the given.

Answer: 3 | Chapter No. 4 |

*Question*

'p is equivalent to q' means ________.

- p is not necessary but p is sufficient for q.
- p is neither necessary nor sufficient for q.
- p is necessary and sufficient for q.
- 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.'

- True
- False

Answer: 2 | Chapter No. 4 |

*Question*

If p is false and q is true, then ~p biconditional q is ______.

- True
- 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 ________.

- False
- True
- Invalid
- Valid

Answer: 4 | Chapter No. 5 |

*Question*

The switches in parallel act just like ________.

- NOT gate
- AND gate
- OR gate
- 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 ?

- A=B
- A=C
- B=C
- 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 _________.

- Tabular form
- Set builder form
- Descriptive form
- A is not a set

Answer: 3 | Chapter No. 7 |

*Question*

If A And B are any two sets, then A-B= B-A

- True
- False

Answer: 2 | Chapter No. 8 |

*Question*

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

- A intersection B
- A union B
- A difference B
- A symmetric difference B

Answer: 2 | Chapter No. 8 |

*Question*

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

- {0,3,90}
- {1,22,34}
- {0,1,3}
- {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}.

- {(a, b, c), (a, b, d)}
- {(a, c, b), (a, d, b)}
- {(b, c, a), (b, d, a)}
- {(c, b, a), (d, b, a)}

Answer: 1 | Chapter No. 11 |

*Question*

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

- x=3 and y=5
- x=4 and y=2
- x=6 and y=12
- 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?

- R is not symmetric
- R is not reflexive
- R is not transitive
- R is reflexive, symmetric and transitive.

Answer: 4 | Chapter No. 12 |

*Question*

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

- Reflexive
- Irreflexive
- Symmetric
- Antisymmetric

Answer: 2 | Chapter No. 14 |

*Question*

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

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

- Reflexive
- Irreflexive
- Symmetric
- Antisymmetric

Answer: 2 | Chapter No. 14 |

*Question*

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

- Reflexive
- Irreflexive
- Symmetric
- 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)}

- R1 and R3 are functions
- R1 and R2 are functions
- R2 and R4 are functions
- 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)}

- x cannot be 2,4 or 5
- x cannot be 4,1 or 6
- x cannot be 2,4 or 6
- 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
- 2
- 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 _________.

- 6
- 8
- 16
- 64

Answer: 2 | 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
- 2
- 4
- 5

Answer: 4 | Chapter No. 15 |

*Question*

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

- Onto
- One to one
- Both one to one and onto
- Neither one to one nor onto

Answer: 1 | Chapter No. 16 |

*Question*

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

- one-One
- identity
- onto
- 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 ε X. Then the function ______ is known as composition of f and g.

- (f o g)
- f
^{-1}(g(x)) - (g o f)
- 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 ______.

- x
- x + 1
- x + 2
- x
^{2}+ 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 _______.

- constant function
- identity function
- bijective function
- injective function

Answer: 2 | Chapter No. 17 |

*Question*

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

- TRUE
- FALSE

Answer: 2 | Chapter No. 17 |

*Question*

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

- empty set or onto
- empty set or one-to-one
- one-to-one or onto
- empty set or 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.

- TRUE
- FALSE

Answer: 1 | Chapter No. 18 |

*Question*

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

- 2
- x
^{2}+ 1 - 2x
^{2}- 1 - 2x
^{2}+ 2

Answer: 4 | Chapter No. 18 |

*Question*

The set Z of all integers is _____.

- uncountable
- 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 _____.

- 2x − 2
- 3x + 2
- 4x + 2
- 3x
^{2}+ 6x

Answer: 4 | Chapter No. 18 |

*Question*

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

- negative real number
- positive real number
- only a real number
- 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)= _________.

- -2
- 6x+2
- 6x-2
- 6x.x-2

Answer: 3 | Chapter No. 18 |

*Question*

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

- 9
- 10
- 11
- infinite

Answer: 3 | Chapter No. 20 |