Discrete Structure (DS) MCQ Questions and answers

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Q. The function f : A → B is injective if whenever f (x)= f (y), where x, y € A, then x = y.

(A) T
(B) F
(C) ---
(D) ---

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Q. Let A be a finite set. If f : A → A is injective then it is surjective.

(A) T
(B) F
(C) ---
(D) ---

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Q. The union of two equivalence relations on a non- empty set is an equivalence relation.

(A) T
(B) F
(C) ---
(D) ---

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Q. If A is a set with 3 elements, how many equivalence relations are there on A? Hint: The set of equivalence classes for a given equivalence relation on A is a partition of the set A.

(A) 4
(B) 5
(C) 23
(D) 29

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Q. Let f: A → B and g: B→C be functions where A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and C = {1, 2, 3, 4, 5, 6}, f =
{(1, 2), (2, 3), (3, 2), (4, 5)} and g = {(1, 3), (2, 4), (3,
5), (4, 6), (5, 1)}. Find g o.f (2).

(A) 3
(B) 4
(C) 5
(D) 6

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Q. A relation R is defined on Z by xRy if 2x +5y = 0(mod7). Then the equivalence class[10] is equal to the equivalence class…

(A) 3
(B) 4
(C) 5
(D) 6

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Q. Let R be a relation on a set A = {1, 2, 3, 4} given by R =
{(1, 1), (1, 2), (1, 3), (2, 1), (2,2), (2, 3), (3, 1), (3, 2), (3,
3)}. Then the relation is:

(A) reflexive and symmetric, but not transitive.
(B) reflexive and transitive, but not symmetric.
(C) symmetric and transitive, but not reflexive.
(D) reflexive, but neither symmetric nor transitive.

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Q. If f (x) = -3x - 5, what is the value of f (2)?

(A) -11
(B) -1
(C) 1
(D) 11

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Q. If g (x) = 3x² - 2x - 5, what is the value of g (-1)?

(A) -4
(B) -10
(C) 6
(D) 0

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Q. Which relation is not a function?

(A) {(2,5), (3,6), (4,7), (5,8)}
(B) {(6,-2), (-4,6), (- 2,4), (1,0)}
(C) {(-1, 5), (-2,5), (- 3,5), (-4,5)}
(D) {(0,-2), (1,0), (-1,- 3), (0,-1)}

Discrete Structure (DS) MCQs with answers Page - 9

Q. The function f : A → B is injective if whenever f (x)= f (y), where x, y € A, then x = y.

Q. Let A be a finite set. If f : A → A is injective then it is surjective.

Q. The union of two equivalence relations on a non- empty set is an equivalence relation.

Q. If A is a set with 3 elements, how many equivalence relations are there on A? Hint: The set of equivalence classes for a given equivalence relation on A is a partition of the set A.

Q. Let f: A → B and g: B→C be functions where A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and C = {1, 2, 3, 4, 5, 6}, f =
{(1, 2), (2, 3), (3, 2), (4, 5)} and g = {(1, 3), (2, 4), (3,
5), (4, 6), (5, 1)}. Find g o.f (2).

Q. A relation R is defined on Z by xRy if 2x +5y = 0(mod7). Then the equivalence class[10] is equal to the equivalence class…

Q. Let R be a relation on a set A = {1, 2, 3, 4} given by R =
{(1, 1), (1, 2), (1, 3), (2, 1), (2,2), (2, 3), (3, 1), (3, 2), (3,
3)}. Then the relation is:

Q. If f (x) = -3x - 5, what is the value of f (2)?

Q. If g (x) = 3x² - 2x - 5, what is the value of g (-1)?

Q. Which relation is not a function?

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Discrete Structure (DS) MCQs with answers Page - 9

Q. The function f : A → B is injective if whenever f (x)= f (y), where x, y € A, then x = y.

Q. Let A be a finite set. If f : A → A is injective then it is surjective.

Q. The union of two equivalence relations on a non- empty set is an equivalence relation.

Q. If A is a set with 3 elements, how many equivalence relations are there on A? Hint: The set of equivalence classes for a given equivalence relation on A is a partition of the set A.

Q. Let f: A → B and g: B→C be functions where A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and C = {1, 2, 3, 4, 5, 6}, f = {(1, 2), (2, 3), (3, 2), (4, 5)} and g = {(1, 3), (2, 4), (3, 5), (4, 6), (5, 1)}. Find g o.f (2).

Q. A relation R is defined on Z by xRy if 2x +5y = 0(mod7). Then the equivalence class[10] is equal to the equivalence class…

Q. Let R be a relation on a set A = {1, 2, 3, 4} given by R = {(1, 1), (1, 2), (1, 3), (2, 1), (2,2), (2, 3), (3, 1), (3, 2), (3, 3)}. Then the relation is:

Q. If f (x) = -3x - 5, what is the value of f (2)?

Q. If g (x) = 3x² - 2x - 5, what is the value of g (-1)?

Q. Which relation is not a function?

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Q. Let f: A → B and g: B→C be functions where A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and C = {1, 2, 3, 4, 5, 6}, f =
{(1, 2), (2, 3), (3, 2), (4, 5)} and g = {(1, 3), (2, 4), (3,
5), (4, 6), (5, 1)}. Find g o.f (2).

Q. Let R be a relation on a set A = {1, 2, 3, 4} given by R =
{(1, 1), (1, 2), (1, 3), (2, 1), (2,2), (2, 3), (3, 1), (3, 2), (3,
3)}. Then the relation is: