2.1 If -Then Statements Objective: State the hypothesis, conclusion and converse of a statement.
If -Then Statements •“If it rains after school, then you will get wet.” •“If you are fourteen, then you are a teenager.”
Breakdown: •“If” called the hypothesis •“Then” called the conclusion •If p, then q. •Also called “conditional” statements
Converse •Switch the hypothesis and the conclusion •If q, then p.
If you are fourteen, then you are a teenager.
•Find the converse: •If you are a teenager, then you are fourteen. •Is it true? •NO!
Counterexample •Proves a statement is false •You could be 13, 15, etc.
Example 1 •Find the converse of “If today is Monday, then tomorrow is Tuesday.” •If tomorrow is Tuesday, then today is Monday. •True!
Biconditional •Both the conditional and the converse are true! •“If and only if” •Written: iff •P iff q.
Example 2
•Create a biconditional statement from example 1. •Today is Monday iff tomorrow is Tuesday. •Tomorrow is Tuesday iff today is Monday.
Work… •If-Then Worksheet •No textbook needed tomorrow.