Proving the Truth of 3(b) in Basic Set Theory

[isabelle york]

how do I go about doing 3(a) and 3(b)?

I'm guessing that for 3(a), it is true, since we have for LHS:

P((A or B) and C)

we can consider the case P(A and C) by excluding B, and this is a subset of the RHS when we also exclude B: (P(A) and P(C)).

We can consider excluding B because it's in an OR function.

Thanks x
isabelle

 

[Office_Shredder]

When you exclude B from the left hand side you make the left hand side smaller - So the question is asking you to show that X is a subset of Y, and you showed that W is a subset of Y where W is a smaller set than X is.

 

[isabelle york]

When you exclude B from the left hand side you make the left hand side smaller - So the question is asking you to show that X is a subset of Y, and you showed that W is a subset of Y where W is a smaller set than X is.

I've managed to do 3(a), it is false. I used the counter example: A= a, B= b, C = a, b.

How do I do 3(b)? 3(b) is 3(a) reversed.

I'm pretty sure 3(b) is true since the RHS will always end up being 'larger', but i don't know how to go about proving it.

EDIT: ignore my reasoning in the OP, I was confused then.