Conditional Statements
(Lesson 6.10)
Honors Math 2
Vocab…
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Conditional Statement
An “If…, then…” statement
-an implication
Example:
If it is raining, then the grass is wet.
More vocab…
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Hypothesis
The “If…” part of a conditional statement
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Example:
…it is raining…
Still more vocab…
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Conclusion:
The “then…” part of a conditional statement
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Example:
…the grass is wet.
Notation
Symbols:
If p, then q.
p is the hypothesis
q is the conclusion
p⇒q
Negation
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It is raining.
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It is not raining
It is not snowing.
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Negation:
Negation:
Symbol:
~
It is snowing
not p is written ~p
Converse
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Statement: If p, then q
p⇒q
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Converse:
€ If q, then p
q⇒ p
Inverse
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Statement: If p, then q
p⇒q
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Inverse:
€
If not p, then not q
~ p ⇒~ q
Contrapositive
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Statement: If p, then q
p⇒q
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Contrapositive:
€
If not q, then not p
~ q ⇒~ p
If you live in this town,
then you live in Massachusetts.
*Is the Inverse true?
live in MA (q)
If you don’t live in this town, then
you don’t live in Massachusetts.
Not necessarily – No!
*Is the Converse true?
live in
this town (p)
If you live in Massachusetts, then
you live in this town.
Not necessarily – No!
*Is the Contrapositive true?
If you don’t live in
Massachusetts, then you don’t
live in this town.
True – Yes!
I always eat cake on my
birthday.
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Hypothesis:
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Conclusion:
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As a conditional statement:
If it is my birthday,
then I will eat cake.
*Is the Inverse true?
I will eat cake (q)
If it’s not my birthday, then I
don’t eat cake.
Not necessarily – nope!
*Is the Converse true?
It is my
birthday (p)
If I eat cake, then it is my
birthday.
Not Necessarily – nope!
*Is the Contrapositive true?
If I don’t eat cake, then it is
not my birthday.
True! – Yes!
Now you try…
n 
With your partner, identify the hypothesis and
conclusion for each of the following statements.
Then, decide whether the statement is true or
false.
n  The base angles of an isosceles triangle are
congruent.
n  Congruent triangles have the same area.
*Is the Inverse true?
*Is the Converse true?
*Is the Contrapositive true?