Set Theory Proofing: Prove that (A ^ B)' ^ B = B ^ A'

[MathMind]

Apologies if this is the incorrect forum for this question..

I would really appreciate some help in proofing the following.

(A ^ B)' ^ B = B ^ A'

Reads as complement of A intersect B , intersected with B, is equal to B intersect A complement.

 

[Deleted member 4993]

Apologies if this is the incorrect forum for this question..

I would really appreciate some help in proofing the following.

(A ^ B)' ^ B = B ^ A'

Reads as complement of A intersect B , intersected with B, is equal to B intersect A complement.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[pka]

Apologies if this is the incorrect forum for this question..
I would really appreciate some help in proofing the following.
\(\displaystyle (A \cap B)^c\cap B = B \cap A^c\)
Reads as complement of A intersect B , intersected with B, is equal to B intersect A complement.

See the quote above. It is a lot more readable is it not?
Here is the code [ tex](A \cap B)^c\cap B = B \cap A^c[/tex](without the first space)

Start with \(\displaystyle (A \cap B)^c = (A^c \cup B^c)\cap B\). Use distribution

 

[stapel]

I would really appreciate some help in proofing the following.

(A ^ B)' ^ B = B ^ A'

Reads as complement of A intersect B , intersected with B, is equal to B intersect A complement.

Try using the standard method of "element-chasing".

Pick a typical, generic element of, say, the left-hand side of the proposed equality. Can you should that this element must necessarily also be an element of the right-hand side? Then you've proved that the left-hand side is a subset of the right-hand side. Then go the opposite direction.

Once you've shown "double set inclusion" (that is, that each set is a subset of the other), then you've proved that the sets must be the same, and are thus equal.

If you get stuck, please reply with a clear listing of your thoughts and steps so far. Thank you!

 

[MathMind]

Thank you, I will try my best to proof it and give you my workings!