# Subsets

• August 9th 2007, 08:23 PM
shilz222
Subsets
Problem: Using truth tables show that $(A \cup C) - B \subseteq (A-B) \cup C$.

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
• August 10th 2007, 02:34 AM
Plato
It is really easy. If there is a T in the $x \in \left( {A \cup C} \right) - B$ column there MUST be a T in the $x \in \left( {A - B} \right) \cup C$ column.