Deductive Reasoning
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Transcript of Deductive Reasoning
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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.
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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?
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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
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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?
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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.
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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.
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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
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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.
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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.
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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.
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Homework
Pg 85 #1-21, 27-32