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SETS
- A collection of elements
- -List method: P={red, blue, yellow}
- -Set Builder Notation: P={x l x is a primary color}
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ELEMENT
E symbol= "is an element of"
-V={8,9,10}
9 E V
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EQUIVELENT SETS
sets that have the same # of elements
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EQUAL SETS
sets that are identicle
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SUBSET
C = if set A contains set B.... B c A
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PROPER SUBSET
- a proper subset is a subset that is not the set itself.
- OR, two sets cannot be equal.
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BINARY AND UNARY
- Has to do with 2 sets....
- Has to do with 1 set.
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UNION
U= The combo of two sets
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INTERSECTION
n= The common elements of two sets
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DISJOINT SETS
- two sets with nothing in common
- (empty set symbol of slashed circle)
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COMPLEMENT
all of the elements NOT given in a set
- u={xlx E colors}
- P={xlx E primary}
- SO.... P'={xlx "slashed element sign" primary}
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Collinear Points
points that lie on the same line
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NONCOLLINEAR POINTS
points that do not lie on the same line
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CONCURRENT LINES
lines that intersect at a single point
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COPLANAR POINTS
points that lie on the same plane
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COPLANAR LINES
Lines that lie on the same plane
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PARRALLEL LINES
coplanar lines that do NOT intersect
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SKEW LINES
lines that are NOT coplanar
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PARALLEL PLANES
planes that do NOT intersect
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POSTULATE
basic statements from which the theorems are proved
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THEOREM
a statement that can be logically proved using a DEFINITION, POSTULATE, or PREVIOUSLY PROVED THEOREM.
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EXPANSION POSTULATE
- a line contains at least 2 points;
- a plane contains at least 3 noncollinear points;
- space contains at least 4 noncoplanar points.
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LINE POSTULATE
any 2 points in space lie in exactly 1 line
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PLANE POSTULATE
3 noncollinear points lie in exactly one plane
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FLAT PLANE POSTULATE
- if 2 points lie in a plane,
- then the line containing these 2 points lie in the same plane
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PLANE INTERSECTION POSTULATE
if 2 planes intersect, than their intersection is exactly 1 line
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THEOREM 1.1
- if any 2 distinct lines intersect,
- they intersect at one & only one point.
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THEOREM 1.2
a line & a point not on that line are contained in one & only one plane
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THEOREM 1.3
2 intersecting lines are contained in one & only one plane
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THEOREM 1.4
2 parallel lines are contained in one & only one plane
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