Question

Let S be the set of all real numbers. Then the relation
R = {(a,b) : 1+ ab> 0} on s is :-
a. reflexive symmetric and transitive
b. reflexive and symmetrie but not transitive
c reflexive and transitive but tot symmetrie
d. symmetric and transitive but not reflexive​

Answer 1

b. reflexive and symmetrie but not transitive.

The relation is given as R = {(a,b) : 1+ ab> 0} o.

Checking for reflexive relation we put R=(a,a)

Putting it in the equation we get 1+a^2 which is Definitely greater than zero

Hence, the relation is reflective.

Now for symmetric relation,

The relation is given as 1+ab>0

Hence, 1+ba>0.

Therefore, the relation is symmetric.

For transitive property,

Given 1+ab>0

Say,1+bc>0

But this doesn't always proove that 1+ca>0

Hence, the relation is not transitive.

Therefore, the relation is symmetric and reflexive but not transitive