NCERT Class 12 Maths Solutions Relations_and_Functions

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NCERT Class 12 Maths Solutions Relations_and_Functions. The NCERT solutions for Class 12 Mathematics have been made by Mathematics teacher of one of the best CBSE school in India. These NCERT solutions have been made to give detailed answers and expanations of the concepts as per NCERT which can be easily understood by the students. Refer to other links also to download mathematics NCERT solutions, worksheets, sample papers and Exemplar Solutions.


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


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