Question

The relation R={(a,b),(b,a)} on set X={a,b} is? A. Reflexive B. Transitive C. Symmetric

Answer 1

A. Relative.

The relation R={(a,b),(b,a)} on set X={a,b} is relative.

Explanation:

R={(a,b): a ≤ b}

If the relation is reflexive,

then (a,a)∈R

Here, a≤a

hence, f(a,a) is true.

So, relation is reflexive.

If the relation is symmetric,

then if (a,b)∈R then(b,a)∈R.

Here, if a≤b then b≤a

For example let's say  a=2,b=5,

2<5 and 5>2

hence, Relation is not symmetric.

Let (a,b)∈R and (b,c)∈R

(a≤b) &  (b≤c).

(a≤c) .

∴(a,c)∈R.

∴R is transitive.