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Deductive Reasoning. 2-3. Deductive Reasoning. The process of reasoning logically from a given statement to a conclusion. Law of detachment – if a conditional’s hypothesis is true, then its conclusion is true If and p is true then so is q. Example 1.

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deductive reasoning1
Deductive Reasoning
  • The process of reasoning logically from a given statement to a conclusion.
  • Law of detachment – if a conditional’s hypothesis is true, then its conclusion is true
  • If and p is true then so is q.
example 1
Example 1
  • Suppose that a mechanic knows that if a car has a dead battery, the car will not start. A mechanic begins to work on a car and finds the battery is dead. What conclusion can she make?
example 2
Example 2
  • Given: If M is the midpoint of a segment, then it divides the segment into two congruent segments.
  • M is the midpoint of AB
example 3
Example 3
  • If a baseball player is a pitcher, then that player should not pitch a complete game two days in a row. Vladimir Nunez is a pitcher. On Monday, he pitches a complete game. What can you conclude?
example 4
Example 4
  • Does the following argument illustrate the Law of Detachment?
  • Given: If it is snowing, then the temperature is less than or equal to 32. The temperature is 20.
  • You conclude: It must be snowing.
example 5
Example 5
  • If possible use the Law of Detachment to draw a conclusion. If it is not possible explain why.
  • Given: If a road is icy, then driving conditions are hazardous. Driving conditions are hazardous.
law of syllogism
Law of Syllogism
  • Allows you to make conclusions about two different conditional statement when the conclusion of one is the hypothesis of the other.
  • If and and p is true, we can use the Law of Syllogism to say that r is also true
example 6
Example 6
  • If a number is prime, then it does not have any repeated factors.
  • If a number does not have any repeated factors, then it is not prime.
  • Draw a conclusion using the law of syllogism.
example 7
Example 7
  • If a number ends in 0 it is divisible by 10
  • If a number is divisible by 10, then it is divisible by 5.
  • If possible, use the Law of Syllogism to draw a conclusion.
example 8
Example 8
  • If a number ends in 6, then it is divisible by 2.
  • If a number ends is 4, then it is divisible by 2.
  • If possible use the Law of Syllogism to to make a conclusion.
homework
Homework
  • Pg 85 #1-21, 27-32
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