Sec. 2.3: Apply Deductive Reasoning Deductive Reasoning uses facts, definitions, accepted properties, and the laws of logic to form a logical argument. - презентация

1 Sec. 2.3: Apply Deductive Reasoning Deductive Reasoning uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

2 Laws of Logic There are two laws of logic that help us draw logical conclusions from information given. The Law of Detachment and the Law of Syllogism.

3 Law of Detachment If the hypothesis (condition) of a true conditional statement is true, then the conclusion is also true. Ex.It is true that if you have a valid California drivers license, then you are allowed to drive in California. If you know Sam has a California drivers license, what can you conclude?

4 Law of Syllogism If you have two true conditional statements where the conclusion of the first is the hypothesis of the second, then you can conclude the hypothesis of the first will result in the conclusion of the second. If p, then q is true, and if q, then r is true, then you can conclude that if p, then r.

5 Syllogism Example Given: If two angles are a linear pair, then they are supplementary. If two angles are supplementary, then their measures add up to 180 degrees Using the Law of Syllogism we can logically conclude that if two angles are a linear pair, then their measures add up to 180 degrees.