This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Types of Statements”.

1. The contrapositive of p → q is the proposition:

a) ¬p → ¬q

b) ¬q → ¬p

c) q → p

d) ¬q → p

View Answer

Explanation: Definition of contrapositive.

2. The inverse of p → q is the proposition:

a) ¬p → ¬q

b) ¬q → ¬p

c) q → p

d) ¬q → p

View Answer

Explanation: Definition of inverse.

3. The converse of p → q is the proposition:

a) ¬p → ¬q

b) ¬q → ¬p

c) q → p

d) ¬q → p

View Answer

Explanation: Definition of converse.

4. 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

View Answer

Explanation: q whenever p contrapositive is ¬q → ¬p.

5. What is the converse of the conditional statement “If it ices today, I will play ice hockey tomorrow.

a) “I will play ice hockey tomorrow only if it ices today.”

b) “If I do not play ice hockey tomorrow, then it will not have iced today.”

c) “If it does not ice today, then I will not play ice hockey tomorrow.”

d) “I will not play ice hockey tomorrow only if it ices today.”

View Answer

Explanation: If p, then q has converse q → p.

6. What are the contrapositive of the conditional statement “I come to class whenever there is going to be a test.

a) “If I come to class, then there will be a test.”

b) “If I do not come to class, then there will not be a test.”

c) “If there is not going to be a test, then I don’t come to class.”

d) “If there is going to be a test, then I don’t come to class.”

View Answer

Explanation: q whenever p, has contrapositive ¬q → ¬p.

7. 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

View Answer

Explanation: p only if q has inverse ¬p → ¬q.

8. What are the converse of the conditional statement “When Raj stay up late, it is necessary that Raj sleep until noon.”

a) “If Raj stay up late, then Raj sleep until noon.”

b) “If Raj does not stay up late, then Raj does not sleep until noon.”

c) “If Raj does not sleep until noon, then Raj does not stay up late.”

d) “If Raj sleep until noon, then Raj stay up late.”

View Answer

Explanation: Necessary condition for p is q has converse q → p.

9. What are the contrapositive of the conditional statement “Medha will find a decent job when she labour hard.”?

a) “If Medha labour hard, then she will find a decent job.”

b) “If Medha will not find a decent job, then she not labour hard.”

c) “If Medha will find a decent job, then she labour hard.”

d) “If Medha not labour hard, then she will not find a decent job.”

View Answer

Explanation: The statement q when p has its contrapositive as ¬q → ¬p.

10. What are the inverse of the conditional statement “If you make your notes, it will be a convenient in exams.”

a) “If you make notes, then it will be a convenient in exams.”

b) “If you do not make notes, then it will not be a convenient in exams.”

c) “If it will not be a convenient in exams, then you did not make your notes.”

d) “If it will be a convenient in exams, then you make your notes

View Answer

Explanation: If p then q has inverse ¬p → ¬q.

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