subset proofs

TonD · #1 $Old$ October 21st, 2009, 10:06 AM

I am a bit confused on how to do proofs with subsets. Here is an example:

Suppose you have 4 sets A, B, C, D

Given A is a subset of B and C is a subset of D, can you prove that (AUC) is a subset of (BUD)? Intuitively, this looks like you can prove it, buy formally I am unsure how to proceed.

Any help/hints are much appreciated.

TonD

CaptainBlack · #2 $Old$ October 22nd, 2009, 07:55 AM

Quote:

Originally Posted by TonD $View Post$

I am a bit confused on how to do proofs with subsets. Here is an example:

Suppose you have 4 sets A, B, C, D

Given A is a subset of B and C is a subset of D, can you prove that (AUC) is a subset of (BUD)? Intuitively, this looks like you can prove it, buy formally I am unsure how to proceed.

Any help/hints are much appreciated.

TonD

suppose $x \in A \cup C$ now show that $x \in B \cup D$

CB

HallsofIvy · #3 $Old$ October 22nd, 2009, 09:22 AM

In other words, use the definition of "subset":
$A\subseteq B$ if and only whenever $x\in A$ , $x\in B$