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If-Then Statements
Contain
2 parts:
The “If” Part:
Hypotheses
The “Then” Part:
Conclusion
If you want your driver’s license,
then you have to pass a
computer test.
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If-Then Statements
All teachers at CATPickering are at least 21
years old.
Write the above as a
conditional statement.
If you are a teacher at CAT-Pickering,
then you are at least 21 years old.
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If-Then Statements
If two angles are
congruent,
Write a conclusion to
this hypotheses…..
then their measures are equal.
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Vertical angles are
formed if two lines
intersect.
What is the hypothesis?
If two lines intersect
Then vertical angles
What is the conclusion?
are formed.
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The “If” Part:
Hypotheses
If you get a Red Rider BB gun for
Christmas,
The “Then” Part:
Conclusion
then you’ll shoot your eye out.
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Is the Converse
True?
Converse: If you shoot
your eye out, you will
get a Red Rider BB gun
for Christmas.
A statement that proves the converse
false is a
counterexample.
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Converse: If you shoot
your eye out, you will
get a Red Rider BB gun
for Christmas.
Here’s a
Counterexample:
I shot my eye out, and I
did NOT get a Red Rider
BB gun for Christmas.
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Law of Syllogism
If p then q.
If q then r.
If p, then r.
If I get an A in geometry this marking
period, then my mom is happy.
If my mom is happy, she buys me a
Lamborghini.
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Law of Syllogism
If I get an A in geometry this marking
period, then …….
My mom buys me a
Lamborghini.
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Law of Syllogism:
You can Skip the
Middle Statement
If I get an A in geometry this marking
period, then my mom is happy.
If my mom is happy, then she buys me
a Lamborghini.
If I get an A in geometry this marking
period, then my mom buys me a
Lamborghini.
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IF You Are Bill Gates, Then You
Have Megabucks.
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IF You Have Megabucks, Then
You Own A Nice House.
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IF You Are Bill Gates, Then You
Own A Nice House.
Medina, Wash.
Gates' 66,000-square-foot
compound is built into a hillside
on the edge of Lake
Washington, near Seattle. Outof-shape visitors can skip the
84-step hike to the ground floor
and opt for an elevator ride
instead. Among its enviable
amenities: a 60-foot swimming
pool with an underwater music
system, a 2,500-square-foot
gym and a 1,000-square-foot
dining room, which seats 24.
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Law of
Detachment
If p then q.
P is true.
So, q must be true.
If it rains, I will cancel my wedding.
It is raining.
I will cancel my wedding.
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Because you
reach a
conclusion from
known facts, you
use…..
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Now try some
problems on
your own.
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