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

The universal relation on a non-empty set A is always:
A) Not Symmetric
B) Not Transitive
C) An Equivalence Relation
D) None of the above

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

A relation R on the set of integers Z is defined by (x, y) ∈ R if |x – y| ≤ 1. The relation R is:
A) Reflexive and Symmetric
B) Reflexive and Transitive
C) Symmetric and Transitive
D) An Equivalence Relation

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

If a relation R on the set {1, 2, 3} is defined by R = {(1, 2)}, then R is:
A) Reflexive
B) Symmetric
C) Transitive
D) None of the above

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

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

A relation R is defined on the set of natural numbers N as (x, y) ∈ R if ‘x is a divisor of y’. The relation R is:
A) Symmetric and Transitive
B) Reflexive and Symmetric
C) Reflexive and Transitive
D) An Equivalence Relation

The function f: R → R defined by f(x) = x² + 1 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

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

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)}