Get Answers to all your Questions

header-bg qa

Please solve RD Sharma maths Class 12 Chapter Relations Exercise 1.1 Question 1 Sub question (iii) maths text book solution.

Answers (1)


Neither reflexive, nor symmetric, not transitive.

Hints :

If R is reflexive \Rightarrow(a, a) \in R \; {\text {for all }} a \in A

If R is symmetric  \Rightarrow(a, b) \in R \Rightarrow(b, a) \in R \text { for all } a, b \in A

If R is transitive  \Rightarrow(a, b) \in R,(b, c) \in R \Rightarrow(a, c) \in R \text { for all } a, b, c \in A

Given :

R=\left\{(x, y): x\; {\text {is wife of }} y\right\}

Solution :

A relation R on set A is said to be reflexive if every element of A is related to itself.

Thus, R is reflexive \Leftrightarrow(a, a) \in R\; {\text {for all }} a \in A.

A relation R on set A is said to be symmetric relation if  (a, b) \in R \Rightarrow(b, a) \in R for all

a, b \in A

i.e; a R b \Rightarrow b R a \text { for all } a, b \in A

 A relation  R on set A is said to be transitive relation if  (a, b) \in R and  (b, c) \in R \Rightarrow (c, a) \in R  for all a, b, c \in A

 i.e; a R b and b R c \Rightarrow a R c for all a, b, c \in A

 For Reflexive:

x is not wife of x and y is not wife of y

 So, R is not reflexive.

For Symmetric:

x is the wife of y but y is not the wife of x.

So, R is not symmetric.

For Transitive:

Let z be a person; \mathrm{z} \in A such that y is the wife of z .

And it is given that x is the wife of y but this case is not possible. Also, here we can’t show x is the wife of z.

So, R is not transitive.

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support