
1 Attachment(s)
Subsets
Problem: Using truth tables show that $\displaystyle (A \cup C)  B \subseteq (AB) \cup C $.
Work/Thoughts: I know that to show that to show that 2 sets are equal, the truth values will be the same. However attached is what I get for the two sets. Some of the truth values are different. Using this how would I conclude that a the first set is a subset of the second set?
Thanks

It is really easy. If there is a T in the $\displaystyle x \in \left( {A \cup C} \right)  B$ column there MUST be a T in the $\displaystyle x \in \left( {A  B} \right) \cup C$ column.