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

Answers (1)


Neither reflexive, nor symmetric nor 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=\{(x, y): x \text { is father of } \mathrm{y}\}

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 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 father of x and  y is not father of y

So, R is not reflexive

For Symmetric:

It is given that x is the father of y.

But we can say that y is not the father of x.

So R is not symmetric.

For Transitive:

 Let z be a person; z \in A such that y is father of z and it is given that x is a father of y.

Then x is grandfather of z

So, R is not Transitive.

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