Explore topic-wise MCQs in Discrete Mathematics.

This section includes 20 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

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
Answer» D. Does not have any counter example
Discussion
2.

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
Answer» C.
Discussion
3.

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
Answer» 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
Discussion
4.

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)
Answer» C. ∀x∀y(x − y = 0)
Discussion
5.

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.
Answer» E.
Discussion
6.

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)
Answer» B. ∀y L(Joy,y)
Discussion
7.

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
Answer» C.
Discussion
8.

“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))
Answer» E.
Discussion
9.

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
Answer» B. For every real number y there exists a real number x such that x is less than y
Discussion
10.

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
Answer» C.
Discussion
11.

DETERMINE_THE_TRUTH_VALUE_OF_‚ÄÖ√Ñ√∂‚ÀւĆ‚ÀÖ√¢N‚ÄÖ√Ñ√∂‚ÀւĆ‚ÀÖ√¢M(N_+_M_=_5_‚ÄÖ√Ñ√∂‚ÀւĆ‚ÀÖ√º_N_‚ÄÖ√Ñ√∂‚ÀւĆ‚Àւ†_M_=_2)_IF_THE_DOMAIN_FOR_ALL_VARIABLES_CONSISTS_OF_ALL_INTEGERS.?$#

A. True
B. False
Answer» C.
Discussion
12.

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 a and b
D. Does not have any counter example
Answer» D. Does not have any counter example
Discussion
13.

Use quantifiers and predicates with more than one variable to express, ‚Äö√Ñ√∂‚àö√ë‚àö‚à´There is a pupil in this lecture who has taken at least one course in Discrete Maths.‚Äö√Ñ√∂‚àö√ë‚àöœ?#

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
Answer» B. ‚Äö√Ñ√∂‚àö‚Ć‚àö√¢x‚Äö√Ñ√∂‚àö‚Ć‚àö√¢yP (x, y), where P (x, y) is ‚Äö√Ñ√∂‚àö√ë‚àö‚à´x has taken y,‚Äö√Ñ√∂‚àö√ë‚àöœÄ the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class
Discussion
14.

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)
Answer» C. ‚Äö√Ñ√∂‚àö‚Ć‚àö√ëx‚Äö√Ñ√∂‚àö‚Ć‚àö√ëy(x ‚Äö√Ñ√∂‚àö‚Ć‚àö‚↠y = 0)
Discussion
15.

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.
Answer» E.
Discussion
16.

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.$

A.
B. ∀x L(x, Joy)
C. ∀y L(Joy,y)
Answer» B. ‚Äö√Ñ√∂‚àö‚Ć‚àö√ëx L(x, Joy)
Discussion
17.

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
Answer» C.
Discussion
18.

“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))
Answer» E.
Discussion
19.

Translate ∀x∃y(x < y) in English, considering domain as 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
Answer» B. For every real number y there exists a real number x such that x is less than y
Discussion
20.

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
Answer» C.
Discussion