Notation
Vocabulary
Subsets & Set Operations
Postulates
Subsets of lines and planes
100
O/
The empty or null set
100
Points that lie on the same line
Collinear
100
Subset, proper subset, or neither?
A={a, b, c} " and " B={x|"x is a letter of the alphabet"}
Proper Subset
100
True or False:
Two lines intersect at two points.
False. According to the Line Intersection Postulate, the intersection of two lines is exactly one point.
200
Translate:
3 in A
3 is an element of set A
200
Noncoplanar lines
Skew lines
200
Subset, proper subset, or neither
A = { } " and " B={"triangle, circle, square"}
Proper subset
200
True or false:
Space contains at least four points.
True by the Expansion Postulate
300
Translate into symbolic notation:
Set A is a proper subset of B.
A sub B
300
These sets are ___________ (equal, equivalent, both or neither.
{a,b,c} and {1, 2, 3}
Equivalent. They have the same number of elements.
300
A uu B
{1,2,3,5,7,9,10}
300
True or false:
Three collinear points determine a plane.
False. According to the Plane Postulate, three noncollinear points determine a plane.
400
Translate into symbolic notation:
The set containing k, l, and m is not a subset of set T
{k,l,m} cancel(sube) T
400
Basic relationships that are assumed to be true without proof
Postulates
400
M'
{1, 3, 5, 7, 9, 11, 13, 15}
400
True or false:
If two points lie in a plane, then the line containing those points lies in the same point.
True by Flat Plane Postulate
500
Translate:
(A uu B)' cancel(sube) S
The complement of A union B is not a subset of set S.
500
lines that intersect at one point
concurrent
500
(A uuB)nnC
{5, 6, 7}
500
How many planes pass through lines AE and AB?
One. A line and a point on that line are contained in one and only one plane.