The smallest equivalence relation on the set A = {a, b, c} is:
A) {(a, a), (b, b), (c, c)}
B) {(a, a), (b, b), (c, c), (a, b), (b, a)}
C) A × A
D) {(a, b), (b, c)}

The relation R on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)} is:
A) Reflexive and Symmetric but not Transitive
B) Reflexive and Transitive but not Symmetric
C) Symmetric and Transitive but not Reflexive
D) An Equivalence Relation

A function f from the set of natural numbers N to the set of integers Z defined by f(n)=(n-1)/2 when n is odd, and f(n)=-n/2 when n is even, is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

The function f: Z → Z defined by f(x) = x³ is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

The function f: R → R defined by f(x) = eˣ is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

A function f is said to be one-to-one (injective) if:
A) f(x_1) = f(x_2 ) implies x_1 ≠ x_2
B) x_1 = x_2 implies f(x_1) ≠ f(x_2)
C) f(x_1) = f(x_2) implies x_1=x_2
D) x_1≠x_2 implies f(x_1)≠f(x_2)

Let R be a relation on a set A such that R = R⁻¹. Then the relation R is:
A) Reflexive
B) Symmetric
C) Transitive
D) Equivalence

The function f: R → R defined by f(x) = 3x + 5 is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

Let R be a relation on the set of human beings in a town at a particular time, given by R = {(x, y) : x is exactly 7 cm taller than y}. This relation is:
A) Reflexive
B) Symmetric
C) Transitive
D) None of the above

The greatest integer function f: R → R, defined by f(x) = [x], is:
A) One-to-one
B) Onto
C) Both one-to-one and onto
D) Neither one-to-one nor onto

Let f: R → R be defined as f(x) = x⁴. Choose the correct answer.
A) f is one-one and onto
B) f is many-one and onto
C) f is one-one but not onto
D) f is neither one-one nor onto

The signum function, f: R → R, given by f(x) = 1 if x > 0, 0 if x = 0, and -1 if x < 0, is: A) One-to-one but not onto B) Onto but not one-to-one C) Both one-to-one and onto D) Neither one-to-one nor onto

The function f: N → N, given by f(n) = n + 1 if n is odd, and f(n) = n – 1 if n is even, is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

Let the function f: N → N be defined by f(x) = 2x. Then f is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

The relation R in the set of real numbers R defined as R = {(a, b) : a ≤ b²} is:
A) Reflexive
B) Symmetric
C) Transitive
D) None of the above