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15 Cards in this Set
- Front
- Back
conditional statement
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consists of two clauses, ohypothesis & conclusion
a → b or "If a, then b." |
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Euler diagrams
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used to see how conditional statements relate to each other
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converse
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converse of conditional statement found by interchanging its hypothesis and conclusion.
The converse of a → b is b → a |
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converse of true statement
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may be false
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For definitions
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converse always true;
a if and only if b a iff b a ↔ b |
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syllogism
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Argument of the form
a → b b → c Therefore, a → c |
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Theorem
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statement that is proved by reasoning deductively from already accepted statements
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Direct proof
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premises lead to conclusion, or theorem
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Indirect proof
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start with assumption that is opposite of desired conclusion, reach contradiction; contradiction will indicate that assumption false and desired conclusion must be true
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postulate
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statement that is assumed to be true without proof
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Postulate 1
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Two points determine a line
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Postulate 2
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Three noncollinear points determine a plane
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Pythagorean Theorem
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The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides
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Triangle Angle Sum Theorem
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The sum of the angles of a triangle is 180º
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Two Circles Theorems
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If the diameter of a circle is d, its circumference is πd.
If the radius of a circle is r, its area is πr². |