# Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following are true?

(i) f is a relation from A to B

(ii) f is a function from A to B

Justify your answer in each case

**Solution:**

It is given that

A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}.

Therefore,

A x B = {(1, 1), (1, 5), (1, 9), (1,11), (1, 15), (1, 16), (2, 1), (2, 5), (2, 9),

(2, 11), (2, 15), (2, 16), (3, 1), (3, 5), (3, 9), (3, 11), (3, 15),

(3, 16), (4, 1), (4, 5), (4, 9), (4, 11), (4, 15), (4, 16)}

**(i)** A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A x B .

It is observed that f is a subset of A x B.

Thus, f is a relation from A to B.

**(ii)** Since the same first element

i.e., 2 corresponds to two different images i.e., 9 and 11.

Thus, f is not a function from A to B

NCERT Solutions Class 11 Maths Chapter 2 Exercise ME Question 10

## Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following are true?(i) f is a relation from A to B.(ii) f is a function from A to B. Justify your answer in each case

**Summary:**

Hence in the first case, f is a function and in the second case, f is a relation from A to B