Welcome to the Logics and Proofs MCQs Page

Dive deep into the fascinating world of Logics and Proofs with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Logics and Proofs, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Logics and Proofs, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

Check out the MCQs below to embark on an enriching journey through Logics and Proofs. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Logics and Proofs. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Logics and Proofs MCQs | Page 7 of 12

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Q61.

The inverse of p → q is the proposition of ____________

¬p → ¬q

¬q → ¬p

q → p

¬q → p

Discuss

Answer: (a).¬p → ¬q

Q62.

The converse of p → q is the proposition of _______________

¬p → ¬q

¬q → ¬p

q → p

¬q → p

Discuss

Answer: (c).q → p

Q63.

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

If it is drizzling, then home team misses

If the home team misses, then it is drizzling

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

If the home team wins, then it is not drizzling

Discuss

Answer: (d).If the home team wins, then it is not drizzling

Q64.

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

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

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

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

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

Discuss

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

Q65.

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

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

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

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

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

Discuss

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

Q66.

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

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

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

None of the mentioned

Discuss

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

Q67.

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

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

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

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

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

Discuss

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

Q68.

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

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

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

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

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

Discuss

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

Q69.

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

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

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

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

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

Discuss

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

Q70.

The compound propositions p and q are called logically equivalent if ________ is a tautology.

p ↔ q

p → q

¬ (p ∨ q)

¬p ∨ ¬q

Discuss

Answer: (a).p ↔ q

Page 7 of 12

Welcome to the Logics and Proofs MCQs Page

Logics and Proofs MCQs | Page 7 of 12

Explore more Topics under Discrete Mathematics

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting Theory

Discrete Probability

Relations

Graphs and Graphs Properties

Tree Properties

Boolean Algebra and Modeling Computations

Group Theory

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