prove that:

A^c ∩ B^c ⊆ (A U B)^c

thank you

Printable View

- May 4th 2010, 08:22 PMslipz418Set Theory Help
prove that:

A^c ∩ B^c ⊆ (A U B)^c

thank you - May 4th 2010, 08:42 PMjakncoke
first of all is c an element or a set?

- May 4th 2010, 08:45 PMslipz418
sorry...i didnt know how to type the complement sign...

- May 4th 2010, 09:41 PMjakncoke
Assume $\displaystyle x \in A^-1 \cap B^-1 . $ By Def, $\displaystyle x \notin A $ and $\displaystyle x \notin B$ so $\displaystyle x \in (U-A-B) $ which means $\displaystyle x \in U - (A + B) = (A \cup B)^{-1} $ remember the distributive laws work on sets.