# Thread: Discrete Math - Cardinals

1. ## Discrete Math - Cardinals

I need to prove this:

if |A\B|=|B\A| then |A|=|B|

The only thing I can see is that this means that I can create a surjective (onto) +injective (one-to-one) function from A to B.

How can I continue solving this?

Thank you very much !

2. what are A and B? Are these sets? Numbers? is || cardinality of sets or absolute value? If they are sets what do you mean A/B are these cosets or what? As it stands your question makes 0 sense to me.

3. A and B are sets. the meaning of | | is cardinality of sets.

A\B is defined as: A ∖ B = A ∩ Bc (c is complement)

4. $\displaystyle |A-B|=|A|-|A\cap B|$
$\displaystyle |B-A|=|B|-|B \cap A|$

If these are the same and we subtract, we get 0 on the LHS and clearly $\displaystyle A\cap B=B\cap A \Rightarrow |A\cap B|=|B\cap A|$

$\displaystyle 0=|A|-|B|\Rightarrow |A|=|B|$

5. Well I really appreciate your good wish to help, but since I posted this on the wrong forum I really couldn't expect to recieve the most percise answers for my problem.

After posting this on the right forum, I got a more percise answer which included ways of solving it that are in my studying material.

Thank you very much anyway