# NCERT Class 12 Maths Solutions Relations and Functions

## 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): 3x 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}

(i) A = {1, 2, 3 … 13, 14}

R = {(x, y): 3x 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

## Books recommended by teachers

 NCERT Class 12 Maths Solutions Relations and Functions
 NCERT Class 12 Maths Solutions Inverse Trigonometric Functions
 NCERT Class 12 Maths Solutions Matrices
 NCERT Class 12 Maths Solutions Determinants
 NCERT Class 12 Maths Solutions Continuity and Differentiability
 NCERT Class 12 Maths Solutions Application of Derivatives
 NCERT Class 12 Maths Solutions Integrals
 NCERT Class 12 Maths Solutions Application of Integrals
 NCERT Class 12 Maths Solutions Differential Equations
 NCERT Class 12 Maths Solutions Vector Algebra
 NCERT Class 12 Maths Solutions Three Dimensional Geometry
 NCERT Class 12 Maths Solutions Linear Programming
 NCERT Class 12 Maths Solutions Probability