# sets

• Aug 17th 2006, 02:46 AM
dcapdogg
sets
Show that AnA'= nullset
• Aug 17th 2006, 04:34 AM
ThePerfectHacker
Quote:

Originally Posted by dcapdogg
Show that AnA'= nullset

If $A=\{ \}$ then proof is complete.
If $A\not = \{\}$ then $x\in A$
Then, $x\not \in A'$ thus, $A\mbox{ and }A'$ are disjoint thus, $A\cap A'=\{\}$
• Aug 17th 2006, 06:30 AM
Soroban
Hello, dcapdogg!

The proof depends upon what axioms and definitions are established.

Quote:

Show that $A \cap A' \:=\:\emptyset$

$A \cap A'$ is the set of elements that are in $A$and in $A'$.

By definition of complement: .If $x \in A$, then $x \not\!\!{\in} A'$
. . Hence, there are no elements common to $A$and $A'.$ .They are disjoint.

Therefore: . $A \cap A' \:= \:\emptyset$