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

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

Answers (1)

Answer : Reflexive, symmetric, transitive.

Hint :

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

Given : R=\{(x, y): x \text { and } y \text { work at same place }\}

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 \Rightarrow(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 \; {\text {and }}\; (b, a) \in R \Rightarrow(c, a) \in R\; {\text {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

Now, let's get back to the actual problem

For Reflexive :

x and x  work at same place

 Similarly, y and y work at the same place. 

 So, R is reflexive.

For Symmetric :

It is given that x and y work at the same place.

So, we can say that y and x work at the same place.

So, R is symmetric.

For Transitive:

Let z be a person such that y and z work at the same place.

And we know that x and y work at the same place.

So, we can say that x and z work at the same place.

So, R is Transitive.

Posted by

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