Venn diagram notes

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The following examples should help you understand the notation, terminology, and concepts related to
Venn diagrams and set notation.
Let's say that our universe contains the numbers 1, 2, 3, and 4. Let A be the set containing the
numbers 1 and 2 that is, A = {1, 2}. (Warning: The curly braces are the customary notation for sets.
Do not use parentheses or square brackets.) Let B be the set containing the numbers 2 and 3 that
is,B = {2, 3}. Then we have the following relationships, with pinkish shading marking the solution
"regions" in the Venn diagrams:
pronunciation meaning Venn diagram answer
A U B "A union B" that is in {1, 2, 3}
either of the sets
A ^ B only the things
or "A intersect B" that are in {2}
both of the sets
A everything
"A complement", in the universe {3, 4}
or "not A"
~A outside of A
everything in A
"A minus B", or
A ­ B except for anything {1}
"A complement B"
in its overlap with B
~(A U B) "not (A union B)" outside {4}
A and B
~(A ^ B) everything outside
or "not (A intersect B)" of the overlap {1, 3, 4}
~( ) of A and B

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