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Sets and Venn Diagrams Solutions

A Venn diagram is a visual tool that uses overlapping circles to represent relationships among sets.
Sets denote groups and compound events .

Parts of a Venn Diagram

The Universal Set	The Subsets
Represented by the rectangle Labeled U in this diagram Includes all elements contained inside it.	Represented by the circles Labeled A and B in this diagram May contain elements in any/all parts of the circle.

Describe the Venn diagram symbolically.

$(A \cup B) ’ = A ’ \cap B ’$

$A \cup B ’$

Shade the Venn diagram to represent the notation.

Note

For the intersection symbol, $\cap,$ you can say “intersects” or the word “and.”

For the union symbol, $\cup,$ you can say “union” or the word “or.”

Venn Diagram	Notation and Wording
$A \subset U, B \subset U$	Subset notation: $\subset$ Sets A and B are subsets of U U includes A and B
$A \cup B$	Union notation: $\cup$ “or” is another word for union The union of A and B Either A or B
$A \cap B$	Intersection notation: $\cap$ “and” is another word for intersection  The intersection of A and B Must include A and B
$A ’$	Complement notation: ’  The complement of A Also said “A not”