Question

A relation R in human being defined as, R = {{a,b): a, b e human
beings: a loves A} is-
(a) reflexive
(b) symmetric and transitive
(c) equivalence
(d) None of these​

Answer 1

Given: A relation R in human being defined as, R = {{a,b): a, b e human

beings: a loves A}

To find: (a) reflexive

             (b) symmetric and transitive

             (c) equivalence

             (d) None of these​

Solution:

For a function to be reflexive, (a,a) both should belong to R

(a loves a) € R is possible as a can love itself. The same goes for b and e and so this is a reflexive function.

For a function to be symmetric, if(a,b)€R then (b, a) should also € to R

This is possible in this case as if a loves b then b will also love a. So the function is symmetric.

For a function to be transitive, if (a,b) and (b,e)€ to R then (a,e) should also € to R. Then, a loves b and b loves e so this also shows that a loves e. Therefore, it is also a transitive function.

The function is (c) equivalence.