Transcript Section 2.1-2.2

Conditional Statement
Geometry
Ms. Olifer
Conditional Statements
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Conditional Statement – if/then form; has
a hypothesis and a conclusion
Inverse
negation of the hypothesis
and conclusion
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Converse
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Contrapositive
switch the conclusion and
the hypothesis
negate the converse
The Parts of Conditional
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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
If it is Saturday, then we will shop.
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Hypothesis:
Conclusion:
Inverse:
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Converse:
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Contrapositive:
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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.
If you see lightening, then you hear
thunder.
You see lightening
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Hypothesis:
Conclusion:
Inverse:
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Converse:
If you hear thunder then you
see lightening.
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Contrapositive:
If you don’t hear thunder then
you won’t see lightening.
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You hear thunder
If you don’t see lightening
then you don’t hear thunder.
Definition
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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.
Important!
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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.
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.
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Hypothesis:
Johnny Depp will star in
Pirates of the Caribbean IV –
The Search for More Dough
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Conclusion:
He won’t have to worry
about money.
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Inverse:
If Johnny Depp does not star
in Pirates of the Caribbean
IV, then he will have to
worry about money.
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.
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Converse:
If he doesn’t have to worry
about money then Johnny
Depp will star in Pirates of
the Caribbean IV.
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Contrapositive:
If he has to worry about money
then Johnny Depp will not star
in in Pirates of the Caribbean IV.