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Prelim Exam in Discrete Math

Total questions: 38

Worksheet time: 41mins

Name
Class
Date
1.

Which of the following propositions is tautology?

a)

(p v q)→q

b)

p v (q→p)

c)

p v (p→q)

d)

Both (b) & (c)

2.

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

a)

a tautology

b)

a contradiction

c)

contingency

d)

all of above

3.

Which of the following statement is a proposition?

a)

Get me a glass of milkshake.

b)

God bless you!

c)

What is the time now?

d)

The only odd prime number is 2

4.

Let P: This is a great website, Q: You should not come back here.

Then "This is a great website and you should come back here.", is best represented by:

a)

~P V ~Q

b)

P ∧ ~Q

c)

P V Q

d)

P ∧ Q

5.

Let P: We should be honest., Q: We should be dedicated .,R: We should be overconfident.

Then "We should be honest or dedicated but not overconfident.", is best represented by:

a)

~P V ~Q V R

b)

P ∧ ~Q ∧ R

c)

P V Q ∧ R

d)

P V Q ∧ ~R

6.

Which of the following bits is the negation of the bits “010110”?

a)

111001

b)

001001

c)

101001

d)

111111

7.

Which of the following option is suitable, if A is “10110110”, B is”11100000”and C is”10100000”, if A XOR B XOR C

a)

010100110

b)

10100000

c)

11110110

d)

11110101

8.

What is the negation of the statement A→(B v C)?

a)

A ∧ ~B ∧ ~C

b)

A→B→C

c)

~A ∧ B v C

d)

None of the mentioned

9.

The compound statement A→ (A→B) is false, then the truth values of A, B are respectively

a)

T,T

b)

F,T

c)

T,F

d)

F,F

10.

Consider the following statements

A: Raju should exercise.

B: Raju is not a decent table tennis player.

C: Raju wants to play good table tennis.

The symbolic form of “Raju is not a decent table tennis player and if he wants to play good table tennis then he should exercise.” is

a)

A→B→C

b)

B∧(C→A)

c)

C→B∧A

d)

B↔A∧C

11.

A compound proposition that is always ___________ is called a tautology.

a)

True

b)

False

c)

Both

d)

None of the above

12.

A compound proposition that is always ___________ is called a contradiction.

a)

True

b)

False

c)

Both

d)

None of the above

13.

The contrapositive of p → q is the proposition:

a)

¬p → ¬q

b)

¬q → ¬p

c)

q → p

d)

¬q → p

14.

The converse of p → q is the proposition:

a)

¬p → ¬q

b)

¬q → ¬p

c)

q → p

d)

¬q → p

15.

What is the contrapositive of the conditional statement? “The home team misses whenever it is drizzling?”

a)

If it is drizzling, then home team misses.

b)

If the home team misses, then it is drizzling.

c)

If it is not drizzling, then the home team does not misses.

d)

If the home team wins, then it is not drizzling.

16.

What are the inverse of the conditional statement “ A positive integer is a composite only if it has divisors other than 1 and itself.”

a)

“A positive integer is a composite if it has divisors other than 1 and itself.”

b)

“If a positive integer has no divisors other than 1 and itself, then it is not composite.”

c)

“If a positive integer is not composite, then it has no divisors other than 1 and itself.”

d)

None of the mentioned

17.

p → q is logically equivalent to:

a)

¬p ∨ ¬q

b)

p ∨ ¬q

c)

¬p ∨ q

d)

¬p ∧ q

18.

Which of the following statement is correct?

a)

p ∨ q ≡ q ∨ p

b)

¬(p ∧ q) ≡ ¬p ∨ ¬q

c)

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

d)

All of mentioned

19.

p ↔ q is logically equivalent to:

a)

(p → q) → (q → p)

b)

(p → q) ∨ (q → p)

c)

(p → q) ∧ (q → p)

d)

(p ∧ q) → (q ∧ p)

20.

If A is “001100” and B is “010101” then A (Ex-or) B is

a)

000000

b)

111111

c)

001101

d)

011001

21.

{x| x is an integer neither positive nor negative} is_________.

a)

Empty set

b)

Non- empty set

c)

Finite set

d)

Both b and c

22.

{x| x is a real number between 1 and 2} is an _________.

a)

Infinite set

b)

Finite set

c)

Empty set

d)

None of the mentioned

23.

Write set {1, 5, 15, 25,…} in set-builder form :

a)

{x| x either x=1 or x=5n, where n is a real number}

b)

{x|x either x=1 or x=5n, where n is a integer}

c)

{x|x either x=1 or x=5n, where n is an odd natural number}

d)

{x| x=5n, where n is a natural number}

24.

Number of power set of {a, b}, where a and b are distinct elements.

a)

3

b)

4

c)

2

d)

5

25.

Subset of the set A= { } is:

a)

A

b)

c)

{∅}

d)

All of the mentioned

26.

A __________ is an ordered collection of objects.

a)

Relation

b)

Function

c)

Set

d)

Proposition

27.

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}

28.

In which of the following sets A- B is equal to B – A

a)

A= {1, 2, 3}, B ={2, 3, 4}

b)

A= {1, 2, 3}, B ={1, 2, 3, 4}

c)

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

d)

A={1, 2, 3, 4, 5, 6}, B ={2, 3, 4, 5, 1}

29.

The shaded area of figure is best described by

a)

A ∩ B

b)

A U B

c)

A

d)

B

30.

The shaded area of figure is best described by

a)

A‘ (Complement of A)

b)

A U B -B

c)

A - B

d)

B-A

31.

The shaded area of figure is best described by

a)

A‘ (Complement of A)

b)

B – (A ∩ B) – (C ∩ B)

c)

A ∩ C ∩ B

d)

B’ (Complement of B)

32.

Let the students who likes table tennis be 12,the ones who like lawn tennis 10,those who like only table tennis are 6,then number of students who likes only lawn tennis are, assuming there are total of 16 students.

a)

16

b)

8

c)

4

d)

10

33.

The shaded area of figure is best described by

a)

A‘ (Complement of A)

b)

A U B – (A ∩ B)

c)

A – B

d)

B

34.

The set containing all the collection of subsets is known as ____________.

a)

Subset

b)

Power set

c)

Union set

d)

None of the mentioned

35.

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}

36.

Two sets are called disjoint if its_____________ is the empty set.

a)

Union

b)

Difference

c)

Intersection

d)

Complement

37.

The set difference of the set A with null set is __________.

a)

A

b)

null

c)

U

d)

B

38.

The set of positive integers is _____________.

a)

Infinite

b)

Finite

c)

Subset

d)

Empty