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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 9 of 12

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Q81.
Let Q(x) be the statement “x < 5.” What is the truth value of the quantification ∀xQ(x), having domains as real numbers.

a.

True

b.

False

c.

May be True or False

d.

Can't say

Discuss
Answer: (b).False
Q82.
Determine the truth value of ∀n(n + 1 > n) if the domain consists of all real numbers.

a.

True

b.

False

c.

May be True or False

d.

Can't say

Discuss
Answer: (a).True
Q83.
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?

a.

True

b.

False

c.

May be True or False

d.

Can't say

Discuss
Answer: (b).False
Q84.
Let R (x) denote the statement “x > 2.” What is the truth value of the quantification ∃xR(x), having domain as real numbers?

a.

True

b.

False

c.

May be True or False

d.

Can't say

Discuss
Answer: (a).True
Q85.
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.

a.

∃x(C(x) ∧ F (x))

b.

∀x(C(x) ∧ F (x))

c.

∃x(C(x) → F (x))

d.

∀x(C(x) → F (x))

Discuss
Answer: (d).∀x(C(x) → F (x))
Q86.
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.

a.

∀x (F (x) → P (x))

b.

∀x (F (x) ∧ P (x))

c.

∃x (F (x) ∧ P (x))

d.

∃x (F (x) → P (x))

Discuss
Answer: (c).∃x (F (x) ∧ P (x))
Q87.
”Everyone wants to learn cosmology.” This argument may be true for which domains?

a.

All students in your cosmology class

b.

All the cosmology learning students in the world

c.

Both of the mentioned

d.

None of the mentioned

Discuss
Answer: (c).Both of the mentioned
Q88.
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.

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

b.

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

c.

All students spends more than 2 hours in playing polo

d.

No student spends more than 2 hours in playing polo

Discuss
Answer: (d).No student spends more than 2 hours in playing polo
Q89.
Determine the truth value of statement ∃n (4n = 3n) if the domain consists of all integers.

a.

True

b.

False

c.

May be True or False

d.

Can't say

Discuss
Answer: (a).True
Q90.
Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A).

a.

True

b.

False

c.

May be True or False

d.

Can't say

Discuss
Answer: (b).False
Page 9 of 12

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