# Proving a set question with three variables

• Oct 16th 2012, 10:34 PM
inflames098
Proving a set question with three variables
Hey guys. New to the math forum. I'm having trouble proving this question. If someone can give just a guide on how to start it, that would assist me with this question and 4 others hopefully.

Let A, B, C be sets. Show that (A∪ B) ⊆ (A ∪ B ∪ C)

I started to to prove the right side by switching the parenthesis, using Associative Law. I used x e A or x e B or x e C (or = the logic upside down carrot symbol)
What do I do from their to prove the left side? Thanks for any input.
• Oct 16th 2012, 11:23 PM
johnsomeone
Re: Proving a set question with three variables
Can you show that \$\displaystyle X \subset X \cup C ?\$ Is it obvious why that's true?

If yes, then look again at \$\displaystyle (A \cup B) \subset (A \cup B \cup C)\$.
• Oct 17th 2012, 08:13 AM
inflames098
Re: Proving a set question with three variables
i guess i was making it to complicated. i see how that will work. thanks man.