Deductive Reasoning and Biconditional Statements · 2014. 1. 24. · For example: If you get caught...

You live in Santa Ana if and only if you live in California.

You go to Segerstrom if and only if you’re in high school.

It is a Jaguar if and only if it roars.

IS THIS BICONDITIONAL TRUE? WHY OR WHY NOT?

A= 20 and B=70 if and only if they are complementary.

Deductive Reasoning

DEDUCTIVE REASONING

using logic to draw conclusions based on accepted statements

LAW OF DETACHMENT

using an accepted statement (rule) to make a conclusion

For example:If you get caught chewing gum, then you get a Saturday school.

If you study your power cards, notes, homework, and go to tutoring, then you will be more successful on the next test that is worth 60% of your overall grade.

If you drink 8 cups of water a day, then you will go numero uno often.

LAW OF SYLLOGISM

if a->b and b->c, then a->c

For example:If he is a pirate, then he has a wooden leg. If he has a wooden leg, then he has splinters.

If he is a rapper, then he wears two chains. If he wears two chains, then his name is Two Chainz.

If he has a mustache, then food gets caught in it. If food gets caught in the mustache, then he has snacks for later.

Deductive vs. Inductive

Law of Detachment

Law of Syllogism

Looking at patterns,

then making conjectures

Randy’s mom gave him 5 dollars, cash money, every week he cleaned his room. He did not clean his room this week, so he is not expecting to get paid 5 dollars, cash money, this week.

If Janet eats a lot of ice cream, then she will become very round. If Janet is round, then she will roll down the hill. If Janet eats a lot of ice cream, then she will roll down the hill.

If you drive over the speed limit, then you will get a speeding ticket. Michael drove over the speed limit and got a speeding ticket.

If you are tardy, then you will get a tardy card. Jermaine was tardy for 2nd period, so Mr. Q gave him a tardy card.

LaToya went to tutoring the day before every test and got an A. She has a test tomorrow and is confident that she is going to get an A because she went to tutoring yesterday.

If Tito is a robot, then he has a lot of lasers. If he has a lot of lasers, then he is dangerous. If Tito is a robot, then he is dangerous.

Write your own scenario using the law of detachment.

Write your own scenario using the law of syllogism.

Write your own scenario using inductive reasoning.

Summary