# Venn Diagram proof?

## Main Question or Discussion Point

Proof for all sets A, B, and C:
A complement U B complement = (A Intercept B) complement.

can someone help??

Related Linear and Abstract Algebra News on Phys.org
Just to the typical point-wise argument. Let x be an element of the LHS and show that implies x is an element of the RHS. Then let x be an element of the RHS and show that implies x is an element of the LHS.

John Venn was a logician who took the standard Euler Diagrams and improved upon them by overlapping and requiring that the overlap be the Union, and that all elements of the sets be constrained to exist in some area of the diagram.

Euler diagrams did not have to overlap, the circles could exist separate from each other. Venn's improvement assisted the logicians with understanding what the Union and disjunctions of sets meant.

Mathematicians then realized their usefulness began using them as well.

Wiki does both okay, but not great:
http://en.wikipedia.org/wiki/John_venn
http://en.wikipedia.org/wiki/Venn_diagram