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Deductive Reasoning
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The Law of Detachment This applies when one statement is conditional and a second statement confirms the hypothesis of the conditional. The conclusion is then confirmed. Here is an example.
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Deductive Reasoning Mary goes to the movies every Friday and Saturday night. Today is Friday. What conjecture can you make from the above statements?
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The Law of Syllogism This applies when you have two conditional statements. The conclusion of one, confirms the hypothesis of the other. In this case our result is still a conditional with the first hypothesis and the second conclusion. (I call this the “Oreo Cookie” Law.) Here is how it works…
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Deductive Reasoning If Rick takes chemistry this year, then Jesse will be Rick’s lab partner. If Jesse is Rick’s lab partner, then Rick will get an A in chemistry. Combine the two above conditional statements into one conditional statement.
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Deductive Reasoning If a polygon is regular, then all angles in the interior of the polygon are congruent. If a polygon is regular, then all of its sides are congruent. Why can’t these two statements be combined like the last example.
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Postulate: Through any two points there exists exactly one line.
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Postulate: A line contains at least two points.
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Postulate: If two lines intersect, then their intersection is exactly one point.
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Postulate: Through any three noncollinear points there exists exactly one plane.
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Postulate: A plane contains at least three noncollinear points.
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Postulate: If two points lie in a plane, then the line containing them lies in the plane.
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Postulate: If two planes intersect, then their intersection is a line.
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