Question

Determine whether the relation R on Q - {0} defined by (a,b)∈ R ⇔ ab= 4 is reflexive,symmetric and transitive.

Answer 1

(a,a)∈ R ⇔ aa= 4 that is a^2 =4 or a = +2 or a=-2 not true for all a ,so its not reflexive.
Symmetric : If (a,b) ∈ R then ab = 4 or ba= 4 that is (b,a)∈ R
Transitivity: (a,b) ∈R and (b,c) ∈R then ab=4 and bc =4 but ac is not equals 4
that is (a,c) doesnt belongs to R so its not transitive
So relation is only symmetric