Relation and Function

NCERT Solution

(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.