Relations and Functions — Practice

Question 1

If A = {a, b} and B = {1, 2, 3}, find n(A × B).

Accepted Answer

n(A × B) = 2 × 3 = 6.

Question 2

Define a one-one and an onto function.

Accepted Answer

One-one: distinct elements have distinct images; onto: every element of the co-domain has a pre-image.

Question 3

If n(A) = 2 and n(B) = 3, find the number of relations from A to B.

Accepted Answer

2^(pq) = 2^6 = 64.

Question 4

If f(x) = x + 3 and g(x) = 2x, find (g ∘ f)(x).

Accepted Answer

(g ∘ f)(x) = g(f(x)) = g(x + 3) = 2(x + 3) = 2x + 6.

Question 5

If n(A) = 3 and n(B) = 2, find the number of functions from A to B.

Accepted Answer

q^p = 2^3 = 8.

Question 6

Is composition of functions commutative?

Accepted Answer

No, in general (f ∘ g) ≠ (g ∘ f).

Practice — Relations and Functions