The first chapter of NCERT Exemplar Solutions for Class 12 Maths is Relations and Functions. This chapter deals with different types of relations and functions.

**NCERT CAREER**

### Q1. If A = {1, 2, 3, 4 }, define relations on A which have properties of being:

(a) reflexive, transitive but not symmetric

(b) symmetric but neither reflexive nor transitive

(c) reflexive, symmetric and transitive.

(c) reflexive, symmetric and transitive.

### Q2. Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:

(a) an injective mapping from A to B

(b) a mapping from A to B which is not injective

(c) a mapping from B to A.

(c) a mapping from B to A.

### Q3. Let * be binary operation defined on R by a * b = 1 + ab, ? a, b ? R. Then the operation * is

(a) commutative but not associative

(b) associative but not commutative

(c) neither commutative nor associative

(d) both commutative and associative

(a) commutative but not associative

### Q4. Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ? a, b ? T. Then R is

(a) reflexive but not transitive

(b) transitive but not symmetric

(c) equivalence

(d) none of these

(c) equivalence

### Q5. Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is

(a) symmetric but not transitive

(b) transitive but not symmetric

(c) neither symmetric nor transitive

(d) both symmetric and transitive

(b) transitive but not symmetric

## Q6. The maximum number of equivalence relations on the set A = {1, 2, 3} are

(a) 1

(b) 2

(c) 3

(d) 5

(d) 5

## Q7. If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is

(a) reflexive

(b) transitive

(c) symmetric

(d) none of these

(d) none of these