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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.

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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.
Which of the following can only be used in disproving the statements?

a.

Direct proof

b.

Contrapositive proofs

c.

Counter Example

d.

Mathematical Induction

Discuss
Answer: (c).Counter Example
Q112.
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 ________

a.

∀nP ((n) → Q(n))

b.

∃ nP ((n) → Q(n))

c.

∀n~(P ((n)) → Q(n))

d.

∀n(~Q ((n)) → ~(P(n)))

Discuss
Answer: (d).∀n(~Q ((n)) → ~(P(n)))
Q113.
When to proof P→Q true, we proof P false, that type of proof is known as ___________

a.

Direct proof

b.

Contrapositive proofs

c.

Vacuous proof

d.

Mathematical Induction

Discuss
Answer: (c).Vacuous proof
Q114.
In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?

a.

Direct proof

b.

Proof by Contradiction

c.

Vacuous proof

d.

Mathematical Induction

Discuss
Answer: (b).Proof by Contradiction
Q115.
A proof covering all the possible cases, such type of proofs are known as ___________

a.

Direct proof

b.

Proof by Contradiction

c.

Vacuous proof

d.

Exhaustive proof

Discuss
Answer: (d).Exhaustive proof
Q116.
Which of the arguments is not valid in proving sum of two odd number is not odd.

a.

3 + 3 = 6, hence true for all

b.

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

c.

All of the mentioned

d.

None of the mentioned

Discuss
Answer: (a).3 + 3 = 6, hence true for all
Q117.
A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as ___________

a.

Direct proof

b.

Contrapositive proofs

c.

Vacuous proof

d.

Proof by cases

Discuss
Answer: (c).Vacuous proof
Q118.
A proof that p → q is true based on the fact that q is true, such proofs are known as ___________

a.

Direct proof

b.

Contrapositive proofs

c.

Trivial proof

d.

Proof by cases

Discuss
Answer: (c).Trivial proof
Q119.
A theorem used to prove other theorems is known as _______________

a.

Lemma

b.

Corollary

c.

Conjecture

d.

None of the mentioned

Discuss
Answer: (a).Lemma
Page 12 of 12

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