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

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)

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

Let A = {1, 2, 3}. Which of the following relations on A is reflexive?
A) {(1, 2), (2, 1), (1, 1)}
B) {(1, 1), (2, 2), (3, 3), (1, 3)}
C) {(1, 1), (2, 2)}
D) {(1, 2), (2, 3), (3, 1)}

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

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

Let R be the relation on set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Which statement is correct?
A) R is reflexive and symmetric but not transitive.
B) R is reflexive and transitive but not symmetric.
C) R is symmetric and transitive but not reflexive.
D) R is an equivalence relation.

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

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

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 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

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

If A = {1, 2, 3} and B = {x, y}, then the total number of functions from A to B is:
A) 6
B) 8
C) 9
D) 3

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