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Define an equivalence relation....

Define an equivalence relation.

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Show that the relation R in the set of all natural number, N defined by is an R = {(a , b) : |a - b| "is even"} in an equivalence relation.

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Show that the relation R in the set A= {1,2,3,4,5} given by R= "{"(a,b):|a-b| is even} is an equivalence relation.

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Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

Let A= {a,b,c}. Which of the following is not an equivalence relation in A?

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Show that the relation R defined in the set A of all polygons as R = {(P _(1), P _(2)): P _(1) and P _(2) have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b) : |a-b| is even}, is an equivalence relation.