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Question
Answer the following:
Show that the following is an equivalence relation
R in A = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}
Solution
a. Since, a = a
∴ (a, a) ∈ R
∴ R is reflexive.
b. Let (a, b) ∈ R
Then a = b
∴ b = a
∴ (b, a) ∈ R
∴ R is symmetric.
c. Let (a, b), (b, c) ∈ R
Then, a = b, b = c
∴ a = c
∴ (a, c) ∈ R
∴ R is transitive.
Thus, R is an equivalence relation.
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