1. Lesson 49
Converse, Contra Positives, If…Then Statements
Text: Chapter 6, section 5
A logical argument consists of a set of premises and conclusions.
PREMISE is the hypothesis and the statement to be arrived at is the
CONCLUSION.
An argument is valid if the conclusion has been arrived at through
accepted forms of reasoning.
The “If…then” statement is called a Conditional Statement and is made
up if the hypothesis (if) and the conclusion (then).
If I do all my assignments then I will have a better pre-calculus mark.
A statement may be TRUE or FALSE.
Example:
If two angles are vertical angles, then they are congruent. (True statement)
Symbolism: p q
Converse: A statement formed by interchanging the hypothesis and
conclusion.
Example:
If two angles are congruent, then they are vertical angles (false statement)
Symbolism: q p
The converse statement may or may not be true.
“If and only if” is used when the converse of a true statement is true.
Example:
A triangle has two equal sides if and only if, it has two equal angles.

2. Symbolism: p q
If the statement is true to create the CONTRA-POSITIVE, you reverse the
hypothesis and the conclusion and negate (turn to a negative word) the
meaning of both hypothesis and conclusion.
Example:
If two angles are not congruent then they are not vertical angles. (True statement)
Symbolism: q p
The contra-positive of a true statement is true and the contra-positive of a
false statement is still false.
To create the Inverse, you negate the hypothesis and the conclusion.
Example:
If the weather is good I will go golfing p q
Inverse – If the weather is NOT good I will NOT go golfing. p q
Example:
If Sunny lives in Plum Coulee, then Sunny lives in Manitoba. Write a Converse,
Inverse and Contra-positive statements:
Converse –
Inverse –
Contra-Positive