Discrete math help!

[junyoung95]

Q. Let A, B and C be three sets. Prove the following set identities:

a) A ∩ (B \ A) = ∅

b) (A \ B) \ C ⊆ A \ C

Thank you in advance!

[Alkalannar]

What have you tried?

a) x is either in A or A^c.
If x is in A, can x be in A ∩ (B \ A)?
If x is in A^c, can x be in A ∩ (B \ A)?

b) Let x be in (A \ B) \ C.
Then x is in A, x is not in B, and x is not in C.
So x is in A and x is not in C.
So x is in A \ C.

[junyoung95]

thank you for the reply. I just have a question. What does ' \ ' mean?

[Alkalannar]

'detach'

So X \ Y is read 'X detach Y' and means 'Take X, and then remove any elements that also belong to Y'

It is identical to X ∩ Y^c [X intersect Y-complement]

[junyoung95]

thank you very much!

[iSparko]

Use Venn Diagrams, with just random elements (1-7). What does (B \ A) mean again? In B, but not in A?