(adsbygoogle = window.adsbygoogle || []).push({}); Help me construct a proof!!

Consider the following set property: For all sets [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex], [tex](A-B) \cup (B-C) = (A \cup B) - (B \cap C)[/tex].

a) Use an element argument to derive this property.

b) Use an algebraic argument to derive this property.

Ok, for part (a), I know that I need to show that:

[tex](A-B) \cup (B-C) \subseteq (A \cup B) - (B \cap C)[/tex], and

[tex](A \cup B) - (B \cap C) \subseteq (A-B) \cup (B-C)[/tex] (right?).

To do this, i need to show that [tex]\forall x[/tex], if [tex]x \ \epsilon \ (A-B) \cup (B-C)[/tex], and [tex]x \ \epsilon \ (A \cup B) - (B \cap C)[/tex]. From here I do not know where to go.

For part (b), any help you can give me I would appreciate. I have written several pages of calculations and have yet to come up with anything.

Please help! This assignment is due 2/25 at 1:30 EST.

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Help me construct a proof

**Physics Forums | Science Articles, Homework Help, Discussion**