# Relation and Function

## NCERT Solution

### Exercise 1.1 Part 2

(v) Relation R in the set A of human beings in a town at a particular time given by Solution: And thus, R is reflexive. Thus, R is symmetric. Therefore, R is transitive

Thus, R is reflexive, symmetric and transitive. Solution: Since, x and x both live in the same locality, Therefore, R is reflexive.

Since, x and y both live in the same locality This means y and x both also live in the same locality

Therefore, R is symmetric Thus, R is transitive.

Thus, R is reflexive, symmetric and transitive. Solution: Here, x is not exactly 7 cm taller than x Thus, R is not reflexive

Now, x is exactly 7 cm taller than y, thus, y is not exactly 7 cm taller than x. Thus, R is not symmetric,

Again, x is exactly 7 cm taller than y and y is exactly 7 cm taller than z, then x would not be 7 cm taller than z

Thus, R is not transitive relation.

Therefore, R is neither reflexive nor transitive and nor symmetric. Solution: Here, it is clear that x is not the wife of x Again, here x is wife of y, but y is not wife of x Thus, R is not symmetric Thus, R is not transitive.

Therefore, R is neither reflexive nor transitive and nor symmetric. Solution: Here, it is clear that x is not the father of x Again, here x is father of y, but y is not father of x Thus, R is not symmetric Thus, R is not transitive.

Therefore, R is neither reflexive nor transitive and nor symmetric.