Question

The relation R defined in the set A = {-1, 0, 1} as R = {(a,b):a = b²}

1. Check whether R is reflexive, symmetric and transitive.

2. Is R an equivalence relation

Answer 1

1. (-1, -1) ∉ R, R is not reflexive

(-1,1) ∈ R but (1, -1) ∉ R, R is not symmetric

(-1,1) ∈ R, (1, 1) ∈ R and (-1, 1) ∈ R,

R is transitive.

2. R is not reflexive, not symmetric and not transitive. So R is not an equivalence relation.