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.

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- April 26th 2010, 07:10 PMtigergirlDefine a relation
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.

- April 26th 2010, 11:10 PMDefunkt
What is the question? (Hi)

- April 26th 2010, 11:14 PMtigergirl
he wants us to find the the relation of this power set?

- April 27th 2010, 08:17 AMMoeBlee
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.