## Relations and Functions Class 12 NCERT Solutions

Class 12 Mathematics students should refer to the following NCERT questions with answers for Relations and Functions in standard 12. These NCERT Solutions with answers for Grade 12 Mathematics will come in exams and help you to score good marks

### Relations and Functions NCERT Solutions Class 12

**MATHS**

**Question 1:**

Determine whether each of the following relations are reflexive, symmetric and transitive:

(i)Relation R in the set *A *= {1, 2, 3…13, 14} defined as

R = {(*x*, *y*): 3*x *− *y *= 0}

(ii) Relation R in the set **N **of natural numbers defined as

R = {(*x*, *y*): *y *= *x *+ 5 and *x *< 4}

(iii) Relation R in the set *A *= {1, 2, 3, 4, 5, 6} as

R = {(*x*, *y*): *y *is divisible by *x*}

(iv) Relation R in the set **Z **of all integers defined as

R = {(*x*, *y*): *x *− *y *is as integer}

(v) Relation R in the set *A *of human beings in a town at a particular time given by

(a) R = {(*x*, *y*): *x *and *y *work at the same place}

(b) R = {(*x*, *y*): *x *and *y *live in the same locality}

(c) R = {(*x*, *y*): *x *is exactly 7 cm taller than *y*}

(d) R = {(*x*, *y*): *x *is wife of *y*}

(e) R = {(*x*, *y*): *x *is father of *y*}

Answer

(i) *A *= {1, 2, 3 … 13, 14}

R = {(*x*, *y*): 3*x *− *y *= 0}

∴R = {(1, 3), (2, 6), (3, 9), (4, 12)}

R is not reflexive since (1, 1), (2, 2) … (14, 14) ∉ R.

Also, R is not symmetric as (1, 3) ∈R, but (3, 1) ∉ R. [3(3) − 1 ≠ 0]

Also, R is not transitive as (1, 3), (3, 9) ∈R, but (1, 9) ∉ R.

[3(1) − 9 ≠ 0]

Hence, R is neither reflexive, nor symmetric, nor transitive.

(ii) R = {(*x*, *y*): *y *= *x *+ 5 and *x *< 4} = {(1, 6), (2, 7), (3, 8)}

It is seen that (1, 1) ∉ R.

∴R is not reflexive.

(1, 6) ∈R

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