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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 10 of 12

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Q91.
“The product of two negative real numbers is not negative.” Is given by?

a.

∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))

b.

∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))

c.

∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))

d.

∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))

Discuss
Answer: (d).∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))
Q92.
Let Q(x, y) be the statement “x + y = x − y.” If the domain for both variables consists of all integers, what is the truth value of ∃xQ(x, 4).

a.

True

b.

False

c.

May be True or False

d.

Can't say

Discuss
Answer: (b).False
Q93.
Let L(x, y) be the statement “x loves y,” where the domain for both x and y consists of all people in the world. Use quantifiers to express, “Joy is loved by everyone.”

a.

∀x L(x, Joy)

b.

∀y L(Joy,y)

c.

∃y∀x L(x, y)

d.

∃x ¬L(Joy, x)

Discuss
Answer: (a).∀x L(x, Joy)
Q94.
Let T (x, y) mean that student x likes dish y, where the domain for x consists of all students at your school and the domain for y consists of all dishes. Express ¬T (Amit, South Indian) by a simple English sentence.

a.

All students does not like South Indian dishes.

b.

Amit does not like South Indian people.

c.

Amit does not like South Indian dishes.

d.

Amit does not like some dishes.

Discuss
Answer: (d).Amit does not like some dishes.
Q95.
Express, “The difference of a real number and itself is zero” using required operators.

a.

∀x(x − x! = 0)

b.

∀x(x − x = 0)

c.

∀x∀y(x − y = 0)

d.

∃x(x − x = 0)

Discuss
Answer: (b).∀x(x − x = 0)
Q96.
Use quantifiers and predicates with more than one variable to express, “There is a pupil in this lecture who has taken at least one course in Discrete Maths.”

a.

∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

b.

∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class

c.

∀x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

d.

∃x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

Discuss
Answer: (a).∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures
Q97.
Determine the truth value of ∃n∃m(n + m = 5 ∧ n − m = 2) if the domain for all variables consists of all integers.

a.

True

b.

False

c.

May be True or False

d.

Can't say

Discuss
Answer: (b).False
Q98.
Find a counter example of ∀x∀y(xy > y), where the domain for all variables consists of all integers.

a.

x = -1, y = 17

b.

x = -2 y = 8

c.

Both x = -1, y = 17 and x = -2 y = 8

d.

Does not have any counter example

Discuss
Answer: (c).Both x = -1, y = 17 and x = -2 y = 8
Q99.
Which rule of inference is used in each of these arguments, “If it is Wednesday, then the Smartmart will be crowded. It is Wednesday. Thus, the Smartmart is crowded.”

a.

Modus tollens

b.

Modus ponens

c.

Disjunctive syllogism

d.

Simplification

Discuss
Answer: (b).Modus ponens
Q100.
Which rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”

a.

Modus tollens

b.

Conjunction

c.

Hypothetical syllogism

d.

Simplification

Discuss
Answer: (a).Modus tollens
Page 10 of 12

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