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Question
Answer the following:
Show that the following is an equivalence relation
R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}
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Solution
a. Clearly (x, x) ∈ R
∴ R is reflexive.
b. If (x, y) ∈ R then (y, x) ∈ R
∴ R is symmetric.
c. Let (x, y) ∈ R, (y, x) ∈ R.
Then x, y, and z are 3 books having same number of pages.
∴ (x, z) ∈ R as x, z have same number of pages.
∴ R is transitive.
Thus, R is an equivalence relation.
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