Premise: If it’s a school day, then I have Geometry class.

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Geometry Chapter 2 Terms.

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Presentation transcript:

Premise: If it’s a school day, then I have Geometry class. Case 1: Given: It is a school day Case 2: Given: I do not have Geometry today. Case 3: Given: If I have Geometry class, then I will need to stay awake.

It is a school day OR it is the weekend. Given: It is not the weekend.

Deductive Reasoning: Drawing Conclusions from Conditionals. If p then q. Law of Detachment If p is true, then q is true. p q p _________ ∴ q

Conditional 1: If you drive at 3:30 you will encounter a lot of traffic. Conditional 2: If you encounter a lot of traffic you will be late for work. Suppose you drive at 3:30, then what?

are true (valid) statements Then we conclude, If p then r Law of Syllogism If If p then q and If q then r are true (valid) statements Then we conclude, If p then r p q q r _________ ∴ p r

If you flunk the test, then you will not graduate. Suppose you will graduate. Contrapositive (Indirect Argument) p q not q _________ ∴ not p

Conditional: Put your coat on or you will freeze. Statement: You don’t put your coat on.

OR conditionals Statement: Given p or q. If one is false the other must be true. p or q not p ∴ q

∴ not p p q p _________ p q not q _________ p or q not p ∴ q p q q r Direct Argument (Law of Detachment) Indirect Argument (contrapositive) p q p _________ ∴ q p q not q _________ ∴ not p Syllogism OR argument p or q not p ∴ q p q q r _________ ∴ p r