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 9 of 12

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Q81.

Determine the truth value of ∀n(n + 1 > n) if the domain consists of all real numbers.

True

False

May be True or False

Can't say

Discuss

Answer: (a).True

Q82.

Let P(x) denote the statement “x = x + 7.” What is the truth value of the quantification ∃xP(x), where the domain consists of all real numbers?

True

False

May be True or False

Can't say

Discuss

Answer: (b).False

Q83.

Let R (x) denote the statement “x > 2.” What is the truth value of the quantification ∃xR(x), having domain as real numbers?

True

False

May be True or False

Can't say

Discuss

Answer: (a).True

Q84.

The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.

∃x(C(x) ∧ F (x))

∀x(C(x) ∧ F (x))

∃x(C(x) → F (x))

∀x(C(x) → F (x))

Discuss

Answer: (d).∀x(C(x) → F (x))

Q85.

The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.

∀x (F (x) → P (x))

∀x (F (x) ∧ P (x))

∃x (F (x) ∧ P (x))

∃x (F (x) → P (x))

Discuss

Answer: (c).∃x (F (x) ∧ P (x))

Q86.

”Everyone wants to learn cosmology.” This argument may be true for which domains?

All students in your cosmology class

All the cosmology learning students in the world

Both of the mentioned

None of the mentioned

Discuss

Answer: (c).Both of the mentioned

Q87.

Let domain of m includes all students, P (m) be the statement “m spends more than 2 hours in playing polo”. Express ∀m ¬P (m) quantification in English.

A student is there who spends more than 2 hours in playing polo

There is a student who does not spend more than 2 hours in playing polo

All students spends more than 2 hours in playing polo

No student spends more than 2 hours in playing polo

Discuss

Answer: (d).No student spends more than 2 hours in playing polo

Q88.

Determine the truth value of statement ∃n (4n = 3n) if the domain consists of all integers.

True

False

May be True or False

Can't say

Discuss

Answer: (a).True

Q89.

Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A).

True

False

May be True or False

Can't say

Discuss

Answer: (b).False

Q90.

Translate ∀x∃y(x < y) in English, considering domain as a real number for both the variable.

For all real number x there exists a real number y such that x is less than y

For every real number y there exists a real number x such that x is less than y

For some real number x there exists a real number y such that x is less than y

For each and every real number x and y such that x is less than y

Discuss

Answer: (a).For all real number x there exists a real number y such that x is less than y

Page 9 of 12

Welcome to the Logics and Proofs MCQs Page

Logics and Proofs MCQs | Page 9 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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