# Relation and Function

## NCERT Exemplar Problem

### Long Answer Type Part 4

Question 25: Functions are defined respectively, by find:

(i) fog

Solution:

(ii) gof

Solution:

(iii) fof

Solution:

(iv) gog

Solution:

Question: 26 – Let * be the binary operation defined on Q. Find which of the following binary operations are commutative.

Solution:

Question: 27 – Let * be binary operation defined on R by Then the operation is:

(i) Commutative but not associative

(ii) associative but not commutative

(iii) neither commutative nor associative

(iv) both commutative and associative.

Answer: (i) is commutative but not associative.

Explanation:

Therefore, * is commutative.

Now, from equation (i) and (ii) it is clear that