# Define a relation

• Apr 26th 2010, 07:10 PM
tigergirl
Define 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 $\displaystyle \approx$ on P(A) defined by $\displaystyle B,C \epsilon P(A)$, $\displaystyle B \approx C$ if and only if B and C contain the same number of elements.
• Apr 26th 2010, 11:10 PM
Defunkt
What is the question? (Hi)
• Apr 26th 2010, 11:14 PM
tigergirl
he wants us to find the the relation of this power set?
• Apr 27th 2010, 08:17 AM
MoeBlee
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.