(A U B) U Cc what will be its venn diagram?????

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- Apr 9th 2009, 03:04 AMadnan1983Venn Diagram
(A U B) U Cc what will be its venn diagram?????

- Apr 9th 2009, 06:10 AMknighty
- Apr 9th 2009, 06:12 AMSoroban
Hello, adnan1983!

Quote:

$\displaystyle A \cup B \cup C\:\!'$

What will be its Venn diagram?

Let: .$\displaystyle S \;=\;A \cup B \cup C\:\!'$

Take the complement of both sides: .$\displaystyle S\:\!' \;=\;\bigg[A \cup B \cup C\:\!'\bigg]\:\!' $

. . DeMorgan's Law gives us: .$\displaystyle S\:\!' \;=\;A' \cap B\:\!' \cap C$

We have: .$\displaystyle S$-complement is the region not in $\displaystyle A$, not in $\displaystyle B$, and in $\displaystyle C.$

. . That is, that region which is in $\displaystyle C$. .(Visualize that region.)__only__

Then $\displaystyle S$ is everythingthat region.**but**