Chapter 2 first quiz Flashcards
Conjecture
Unproven statement based on observation (guessing)
Inductive Reasoning
Use of examples and patterns to make a guess about something (form conjecture)
Counterexample
Specific example that proves a conjecture false
Deductive Reasoning
Use of facts, definitions, and accepted properties in logical order to write a logical argument
Law of Detachment
If p –> q is true and p is true… then q is true.
You have to know the hypothesis to know the conclusion.
hypothesis-conclusion hypothesis conclusion
Law of Syllogism
If p –> q and q –> r are true conditional then p –> r is true
If you take computer essentials, then you are in 4th hr.
If you are in 4th hr, then I despise you.
ab + bc =ac
Determinance Post. 1 (Two point post.)
Through any two points exists exactly one line
Through A and B exists line l
Existance Post. 1 (Line pt. -post)
A line contains at least two points
line l contains pts. A and B
Intersection Post. 1 (Line - Int. Post.)
If two lines intersect then the intersection is exactly one point.
<–> AB and <–> BC intersect at E
Determinance Post 2. (3 pt. post.)
Through any three non-collinear pts. there exists exactly 1 plane.
Through points A, B, and C exist plane P.
Existance post. 2 (Plane - pt. post.)
A plane contains at least 3 non-colinear pts.
Plane p contains pts A, B, and C
Intersection Post. 2 (Plane - int. post)
If two planes intersect, then the intersection is a line.
Points A and B lie on plane p. Therefore, <–> AB lies on plane p.
Determinance Post. 3
If two pts. lie in a plane, then the line connecting them lies in the same plane.
If you have two points and connect them that makes a line.
The line is on the plane.
Perpendicular line to a plane
A line is perpendicular to a plane if it intersects at 1 pt. and is perpendicular to every line that goes through that point.
1
2
3
1: They have one dimension. A line is one dimension.
2: They have two dimensions. A plane is two dimensions.
3: They have both. A plane (two) and a line (one) equal three.
