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If x + 9 = 14y, then 14y = x + 9
------------> Symmetric Property

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The law of syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form: P → Q. Q → R.

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Subtraction Property
Addition Property
Multiplication Property
Division Property
Reflexive Property
Symmetric Property
Transitive Property
Substitution Property

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A counterexample is a special kind of example that disproves a statement or proposition. Counterexamples are often used in math to prove the boundaries of possible theorems

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an opinion or conclusion formed on the basis of incomplete information.

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converse: if q then p
Inverse: if not p, then not q
Contrapositive: if not q, then not p