UPSC NDA I 2015 Mathematics Solved Paper

(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.