**Solution:**

(x,y)are related as x<y

⇒y>x+5

Reflexive :

For (x,x) to be in th relation,x>x+5.

The above condition is not true.

Hence, the relation is not reflexive.

Symmetric:

If (x,y) belongs to the relation, then

y>x+5....(1)

For (y,x) to be in the relation,x>y+5

The above does not follow from (1).

Hence, (y, x) does not belong to the relation.

Hence, the relation is not symmetric.

Transitive:

If (x, y) and (y, z) belong to the relation,then

y>x+5 and

z>y+5

⇒z>x+5+5

⇒z>x+5

Hence, (x, z) belongs to the relation.

∴ (x, y) and (y, z) belong to the relation

⇒ (x, z) belongs to the relation.

Hence, the relation is transitive.

So the relation is transitive but neither reflexive nor symmetric.

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