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Deductive Reasoning 2-3
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Deductive Reasoning
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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
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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
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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
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