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