1. SET: A collection of things.
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ELEMENT: |
An element is MEMBER of a SET. It is denoted by the symbol  |
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If something is NOT AN ELEMENT of a ser we use the symbol |
3. The NOTATION for sets are BRACES, { }
Example: {Jan., Feb., Mar.} The set of the first three months of the year.
Example: {a, e, i, o, u} The set of the vowels in the English language.
4. CAPITAL letters are used to name a set:
Example: A = {Jan., Feb., Mar.}
B = {a, e, i, o, u}
5. SUBSET: If every element in a given set B is also an element of a set A, then B is a
SUBSET of A.
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Example: |
B A means "B is a SUBSET of A."
If H = {1, 2, 3, 4, 5, 6} and
K = {2, 4, 6}
then K H
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Note 1 |
If there is at least one element of B that is not in A then B is NOT A SUBSET of A.
This is written B A |
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Example: |
If H = {1, 2, 3, 4, 5, 6} and
M = {5, 7, 9}
then M H |
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Note 2 |
Every set is a subset of itself. |
6. The NULL or EMPTY SET is a set which contains NO ELEMENTS.
The symbol for the empty set is f the Greek letter Phi or we may just write { }.
7. The UNIVERSE or UNIVERSAL SET is the set which contains all the
elements under discussion. The symbol for the UNIVERSAL SET is 8. The COMPLEMENT of a set A is the set of all elements in the UNIVERSAL SET
which are NOT in the set A.
The COMPLEMENT of a set is denoted as A' and can be read as "A complement,"
"the complement of A," or "A prime."
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Example: |
If U = {a, e, i, o, u} and
A = {a, i, u}
then A' = {e, o},
since the elements"e" and "o" are the only elements that are NOT in A but yet are in the Universal Set U. |
9. The UNION of sets A and B, A B, is the set containing all the
elements that are members of set A OR set B. 10. The INTERSECTION of two sets A and B, A B , is the set containing
all the elements that are common to BOTH sets A AND set B.
Below is an example of UNION and INTERSECTION using the following sets:
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 4, 6}
B = {1, 3, 6, 7, 9}
C = { }
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