# Set Theory Help

• May 4th 2010, 08:22 PM
slipz418
Set Theory Help
prove that:

A^c ∩ B^c ⊆ (A U B)^c

thank you
• May 4th 2010, 08:42 PM
jakncoke
first of all is c an element or a set?
• May 4th 2010, 08:45 PM
slipz418
sorry...i didnt know how to type the complement sign...
• May 4th 2010, 09:41 PM
jakncoke
Assume $x \in A^-1 \cap B^-1 .$ By Def, $x \notin A$ and $x \notin B$ so $x \in (U-A-B)$ which means $x \in U - (A + B) = (A \cup B)^{-1}$ remember the distributive laws work on sets.