1. Conditional Statement Geometry Ms. Olifer

2. Conditional Statements
Conditional Statement – if/then form; has a hypothesis and a conclusion
Inverse
Converse
Contrapositive
negation of the hypothesis and conclusion
switch the conclusion and the hypothesis
negate the converse

3. The Parts of Conditional
In an if-then statement, the clause following the “if” is called the hypothesis.
The clause following the “then” is the conclusion.
Ex. If a figure is a segment, then it’s a convex set.
hypothesis conclusion

4. If it is Saturday, then we will shop.
Hypothesis:
Conclusion:
Inverse:
Converse:
Contrapositive:
It is Saturday
We will shop
If it isn’t Saturday then we will not shop.
If we shop then it is Saturday.
If we don’t shop, then it isn’t Saturday.

5. If you see lightening, then you hear thunder.
Hypothesis:
Conclusion:
Inverse:
Converse:
Contrapositive:
You see lightening
You hear thunder
If you don’t see lightening then you don’t hear thunder.
If you hear thunder then you see lightening.
If you don’t hear thunder then you won’t see lightening.

6. Definition
An instance of a conditional is a specific case in which both the antecedent (if part) and the consequent (then part) of the conditional are true.
A counterexample to a conditional is a specific case for which the antecedent (if part) of the conditional is true and its consequent (then part) is false.

7. Important!
If a given conditional statement is true, the converse and inverse are not necessarily true.
However, the contrapositive of a true conditional statement is always true, and the contrapositive of a false conditional is always false.

8. If Johnny Depp will star in Pirates of the Caribbean IV, The Search for More Dough, then he won’t have to worry about money.
Johnny Depp will star in Pirates of the Caribbean IV – The Search for More Dough
Hypothesis:
Conclusion:
Inverse:
He won’t have to worry about money.
If Johnny Depp does not star in Pirates of the Caribbean IV, then he will have to worry about money.

9. If Johnny Depp will star in Pirates of the Caribbean IV, The Search for More Dough, then he won’t have to worry about money.
Converse:
Contrapositive:
If he doesn’t have to worry about money then Johnny Depp will star in Pirates of the Caribbean IV.
If he has to worry about money then Johnny Depp will not star in in Pirates of the Caribbean IV.