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 12 of 12

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Q111.

Let the statement be “If n is not an odd integer then sum of n with some not odd number will not be odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some not odd number will not be odd.” A proof by contraposition will be ________

∀nP ((n) → Q(n))

∃ nP ((n) → Q(n))

∀n~(P ((n)) → Q(n))

∀n(~Q ((n)) → ~(P(n)))

Discuss

Answer: (d).∀n(~Q ((n)) → ~(P(n)))

Q112.

When to proof P→Q true, we proof P false, that type of proof is known as ___________

Direct proof

Contrapositive proofs

Vacuous proof

Mathematical Induction

Discuss

Answer: (c).Vacuous proof

Q113.

In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?

Direct proof

Proof by Contradiction

Vacuous proof

Mathematical Induction

Discuss

Answer: (b).Proof by Contradiction

Q114.

A proof covering all the possible cases, such type of proofs are known as ___________

Direct proof

Proof by Contradiction

Vacuous proof

Exhaustive proof

Discuss

Answer: (d).Exhaustive proof

Q115.

Which of the arguments is not valid in proving sum of two odd number is not odd.

3 + 3 = 6, hence true for all

2n +1 + 2m +1 = 2(n+m+1) hence true for all

All of the mentioned

None of the mentioned

Discuss

Answer: (a).3 + 3 = 6, hence true for all

Q116.

A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as ___________

Direct proof

Contrapositive proofs

Vacuous proof

Proof by cases

Discuss

Answer: (c).Vacuous proof

Q117.

A proof that p → q is true based on the fact that q is true, such proofs are known as ___________

Direct proof

Contrapositive proofs

Trivial proof

Proof by cases

Discuss

Answer: (c).Trivial proof

Q118.

A theorem used to prove other theorems is known as _______________

Lemma

Corollary

Conjecture

None of the mentioned

Discuss

Answer: (a).Lemma

Page 12 of 12

Welcome to the Logics and Proofs MCQs Page

Logics and Proofs MCQs | Page 12 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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