Proving Set Relationships

Hello everyone,

I'm stuck on this problem, not sure where to start, any help would be appreciated. I don't know how to put in the "is a subset" symbols in this but hopefully I can explain it well enough for you to understand:

For all subsets A,B, and C of some universal set U, A "is a subset" of B U C if and only if A "is a subset" B or A "is a subset" C.

Of course, the U between the B and C is a union, in case that threw some people off.

Thanks!

Re: Proving Set Relationships

Re: Proving Set Relationships

Quote:

Originally Posted by

**Measure13** For all subsets A,B, and C of some universal set U, A "is a subset" of B U C if and only if A "is a subset" B or A "is a subset" C.

This is false. Take any two nonempty disjoint sets B and C and let A = B ∪ C.