1. ## subset proofs

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

2. Originally Posted by TonD
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 $\displaystyle x \in A \cup C$ now show that $\displaystyle x \in B \cup D$

CB

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