Deductive reasoning
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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 Reasoning

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Deductive reasoning

Deductive Reasoning

2-3


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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