This document discusses conditional statements and their logical variations. It begins by stating that conditional statements are crucial to understanding truth and are used in many fields. It then lists objectives related to identifying conditional statements and converting them between logical forms. The document goes on to define conditional statements, discuss converting statements not in if-then form to conditional form, and explain the converse, inverse, and contrapositive of conditional statements. It concludes by listing several point, line and plane postulates of geometry.

1. Unit 2. Section 2.1
CONDITIONAL STATEMENTS

2. - Conditional statements are used in every field
of human endeavor.
- They are crucial to the search for truth
- If you are going to be able to adequately
interpret and judge the statements you hear,
you must understand the structure of
Conditional statements.
-
WARNING: Once you get good at these, you
may be amused by statements made by
politicians and other public speakers.

3. Objectives
 Students will be able to:
 Identify conditional statements and place them in
if-then form
 Identify the hypothesis and conclusion of a
conditional statement
 Convert conditional statements into their other
logical variants
 Identify and use truth relationships of conditional
statements
 State and use the point, line and plane postulates
of geometry

4. What is a Conditional
Statement?
 A statement that can be written in the
format:
If …., then ….
 The part after “if” is called the hypothesis
 Do not confuse this with the word “hypothesis”
from science
 The rest (after “then”) is the conclusion

5. Statements Not in If-Then Form
- Often statements are not in if –then form, but to
test them out scientifically, we must convert them
- In English, there are infinite ways to rephrase a
conditional statement; however, we will cover the
three most common variations here

6. Standard Sentence
 Split the subject and predicate.
 Add “If it is” or “If they are” to the subject
 Add “then it” or “then they” to the predicate
 Smooth out the grammar
 Example: “All dogs go to heaven.”
 “If they are dogs, then they go to heaven.”

7. “Whenever” or “When”
 Replace “whenever” or “when” with “if”
 Add “then” after the comma
 Example: “Whenever I see a seagull, I think of
home.”
 If I see a seagull, then I think of home.

8. “If” at the end
 Move the “if” clause to the beginning
 Add “then” after the “if” clause
 Example: “I eat if I am hungry.”
 “If I am hungry, then I eat.”

9. Logical Variations of the
Conditional
-Often a conditional statement can be difficult to
prove or unwieldy to use.
- By using logical variations, we find forms easier to
prove or use.

10. Converse, Inverse, &
Contrapositive
 Converse: formed by swapping the
hypothesis and the conclusion
 Inverse: formed by negating the hypothesis
and conclusion
 Contrapositive: formed by both negating and
swapping the hypothesis and conclusion

11. Equivalent Statements
 If the Conditional is true (or false) then so is
the Contrapositive and vice versa.
 Similarly, if the Converse is true, then so is the
Inverse and vice versa
 If both the Conditional and its Converse are
true, then they can be rewritten as a
Biconditional statement (more next class)

12. Example 1
 If you added 2+2, you got 4
 CONVERSE:
If you got 4, then you added 2+2.
 INVERSE:
If you did not add 2+2, you did not get 4.
 CONTRAPOSITIVE:
If you did not get 4, then you did not add 2+2.

13. Example 2 (the word “not”)
 If you do not eat, you will be hungry
 CONVERSE:
If you are hungry, then you did not eat.
 INVERSE:
If you ate, then you are not hungry.
 CONTRAPOSITIVE:
If you are not hungry, then you ate.

14. Point, Line and Plane Postulates

15. Point, Line & Plane Postulates
5. Through any two points there exists exactly one line.
6. A line contains at least two points.
7. If two lines intersect, then their intersection is exactly
one point.
8. Through any three noncollinear points there exists
exactly one plane.
9. A plane contains at least three noncollinear points.
10. If two points lie in a plane, then the line containing
them lies in the plane.
11. If two planes intersect, then their intersection is a
line.

16. Reference
 McDougal Littell Geometry (2001), Section
2.1