Discrete Mathematics Questions and Answers – Logics – Nested Quantifiers

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Logics – Nested Quantifiers”.

1. 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
View Answer

2. Translate ∀x∃y(x < y) in English, considering domain as a real number for both the variable.
a) For all real number x there exists a real number y such that x is less than y
b) For every real number y there exists a real number x such that x is less than y
c) For some real number x there exists a real number y such that x is less than y
d) For each and every real number x and y such that x is less than y
View Answer

3. “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))
View Answer

4. 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
View Answer

5. 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)
View Answer

6. 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.
View Answer

7. 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)
View Answer

8. 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
View Answer

9. 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
View Answer

10. Find a counterexample 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
View Answer

Sanfoundry Global Education & Learning Series – Discrete Mathematics.

To practice all areas of Discrete Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.