Thread: How would you prove...

How would you prove that

(A/B) U B = A if and only if B C A ?

It's the iff that is giving me problems. Is there a technique for this type of proof?

Originally Posted by Cairo

How would you prove that
(A/B) U B = A if and only if B C A ?

There is no one way to do any set theory proof.
Here you might note that

Starting with what would

Originally Posted by Cairo

How would you prove that

(A/B) U B = A if and only if B C A ?

It's the iff that is giving me problems. Is there a technique for this type of proof?

This statement is equivalent to the following statement :

iff

Originally Posted by princeps

This statement is equivalent to the following statement :

iff

Thanks, but this looks even worse to me!

Would this not be A, Plato?

I was thinking of relabelling (B C A) as D and ((A/B) U B = A) as E and then trying to argue D implies E and also that ~D implies ~E, but not sure if this would work or even where to start.

Originally Posted by Cairo

Would this not be A, Plato?

That is correct. So you have proved it one way.

Now suppose that now show that

Originally Posted by Plato

That is correct. So you have proved it one way.

Now suppose that now show that

Using the distributive law I get

(A U B) and (B^c U B) = .......

But not sure how to continue this argument.

Will have a think about it.

Originally Posted by Plato

There is no one way to do any set theory proof.
Here you might note that

Starting with what would

Should not be

And then be equal to: ?