Let A={a,b,c} and P(A) be the power set of A ( the family of subsets of A)
Define the relation on P(A) defined by , if and only if B and C contain the same number of elements.
Maybe you mean he wants you to explicitly LIST the members of the relation.
Let A = {a b c}
PA = {0 {a} {b} {c} {a b} {a c} {b c} {a b c}}
Let R = {<x y> | x in PA, y in PA, and x and y are equinumerous}
So R =
{<0 0>
<{a} {a}>
<{b} {b}>
<{c} {c}>
<{a} {b}>
<{b} {a}>
<{a} {c}>
<{c} {a}>
<{b} {c}>
<{c} {b}>
<{a b} {a b}>
<{a c} {a c}>
<{b c} {b c}>
<{a b} {a c}>
<{a c} {a b}>
<{a b} {b c}>
<{b c} {a b}>
<{a c} {b c}>
<{b c} {a c}>
<{a b c} {a b c}>}
That was boring. I have no idea why I bothered doing it.