Question

Let R = {(3, 3) (6, 6) (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set 

A = {3, 6, 9, 12}. The relation is 

(a) reflexive and symmetric only 

(b) an equivalence relation 

(c) reflexive only 

(d) reflexive and transitive only.

Answer 1

(d) : For (3, 9) ∈ R, (9, 3) ∉ R 

Therefore,relation is not symmetric which means our choice 

(a) and (b) are out of court. We need to prove reflexivity and transitivity. 

For reflexivity a ∈ R, (a, a) ∈ R which is hold i.e. R is reflexive. Again, 

for transitivity of (a, b) ∈ R , (b, c) ∈ R 

=> (a, c) ∈ R 

which is also true in R = {(3, 3)(6, 6), (9, 9), (12, 12), (6,12), (3, 9), (3, 12), (3, 6)}.