NCERT Class 12 Maths Solutions Relations and Functions

NCERT Class 12 Maths Solutions Relations and Functions with answers available in Pdf for free download. The NCERT Solutions for Class 12 Mathematics with answers have been prepared as per the latest syllabus, NCERT books and examination pattern suggested in Standard 12 by CBSE, NCERT and KVS. Solutions to questions given in NCERT book for Class 12 Mathematics are an important part of exams for Grade 12 Mathematics and if practiced properly can help you to get higher marks. Refer to more Chapter-wise Solutions for NCERT Class 12 Mathematics and also download more latest study material for all subjects

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}

Answer

(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

 

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