Prove that for any sets A, B, C, D;
(AxB)U(CxD) is a subset of (AUC) x (BUD).
Give an example to show that the reverse inclusion need not hold.
Write in symbolic form what the following means.
1. A subset (every element of one set is an element of the other).
2. An element of (AxB)U(CxD)
3. An element of (AUC) x (BUD).
The result should be a proposition consisting of logical connectives and things like or . Is this proposition true?
You will not be able to solve this problem until you know the definitions of a subset, a Cartesian product and a union and are able apply those definitions to this situation.