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