2.3 Apply Deductive Reasoning

[Pages:10]Notes 2.3

September 27, 2016

2.3 Apply Deductive Reasoning Deduc&ve Reasoning

Defini&on: Use facts, definitions, and logic to form a logical argument.

Example: Newton's Law says that everything that goes

up must come down. And so, if you kick the ball up, it must come down.

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September 27, 2016

Induc&ve Reasoning

Defini&on: Use specific examples and patterns to form a conclusion.

Example: I've noticed previously that every time I kick a ball up, it

comes back down, so I guess this next time when I kick it up, it will come back down, too.

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September 27, 2016

Example 1:

Which of the following would be best expressed by inductive reasoning ?

a) Your first quiz grade usually indicates how you will do in the course.

b) The final exam accounts for 30% of the course grade.

c) Late papers will not be accepted

d) Gravity's Rainbow is required reading in your course.

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September 27, 2016

Example 2:

Which of the following would be best expressed by deductive reasoning ?

a) There was a mild winter this year, and previously whenever there's been a cold winter the cherry crop suffers.

b) The cherry crop needs at least a week of freezing temperatures for best results, and this winter the temperature stayed several degrees above freezing.

c) Jack noticed that whenever the skiing was good in the winter, the cherry crop was profitable, and this year the skiing was good.

d) Not since 1972 have I seen a good cherry crop after mild winter, and this winter has been mild.

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September 27, 2016

Example 3: Decide whether the following represents induc&ve or deduc%ve reasoning.

All reptiles are cold-blooded. Parrots are not cold-blooded. Sue's pet parrot is not a reptile.

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September 27, 2016

Law of Syllogism

Example 4: All squares are rectangles. All rectangles have four sides. So, all squares have four sides.

Example 5: My best friend is a redskins fan. All redskins fans annoy my brother. So, ___________________________.

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September 27, 2016

Example 6: If possible use the law of syllogism to write a new condi7onal statement that follows.

a) If Rick takes chemistry this year, then Jesse will be

Rick's lab partner. If Jesse is Rick's lab partner, then Rick will get an A in chemistry.

b) If a polygon is regular, then all angles in the interior of the

polygon are congruent. If a polygon is regular, then all of its sides are congruent.

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September 27, 2016

You try...

If possible use the law of syllogism to write a new condi7onal statement that follows.

a) If Jenelle gets a job, then she can afford a car. If Jenelle can afford a car, then she will drive to school.

b) If you get an A or better on your math test, then you can go to the movies. If you go to the movies, then you can watch your favorite actor.

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