1. Conditional Statements
Section 2-3

2. Conditional Statements
If-then statements are called conditional statements.
The portion of the sentence following if is called the hypothesis. The part following then is called the conclusion.
p q (If p, then q)

3. If it is an apple, then it is a fruit.
Hypothesis – It is an apple.
Conclusion – It is a fruit. p q

4. Converse q p
The converse statement is formed by switching the hypothesis and conclusion.
If it is an apple, then it is a fruit.
Converse: If it is a fruit, then it is an apple.
The converse may be true or false.

5. negation – the denial of a statement
Ex. “An angle is obtuse.”
Negation – “An angle is not obtuse.”

6. Inverse ~p ~q
An inverse statement can be formed by negating both the hypothesis and conclusion.
If it is an apple, then it is a fruit.
Inverse: If it is not an apple, then it is not a fruit.
The inverse may be true or false.

7. Contrapositive ~q ~p
A contrapositive is formed by negating the hypothesis and conclusion of the converse.
If it is an apple, then it is a fruit.
Contrapositive: If it is not a fruit, then it is not an apple.
The contrapositive of a true conditional is true and of a false conditional is false.