Reasoning and proof

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What is the Symmetric Property of Equality?

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If a = b, then b = a. This property states that if one quantity equals another, then the second quantity equals the first.

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What is the Converse of a statement?

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The converse of a statement 'If p, then q' is 'If q, then p'. It switches the hypothesis and conclusion.

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What is the Contrapositive of a statement?

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The contrapositive of a statement 'If p, then q' is 'If not q, then not p'. It negates both the hypothesis and conclusion and switches them.

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What is a Counterexample?

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A counterexample is an example that disproves a conjecture or statement. It shows that the statement is not always true.

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What is the Reflexive Property of Equality?

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For any number a, a = a. This property states that any quantity is equal to itself.

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What is the Transitive Property of Equality?

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If a = b and b = c, then a = c. This property allows us to conclude that if two quantities are each equal to a third quantity, they are equal to each other.

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What is Inductive Reasoning?

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Inductive reasoning involves making generalizations based on specific observations or patterns.

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What is Deductive Reasoning?

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Deductive reasoning involves starting with general statements or principles and applying them to specific cases to reach a conclusion.

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What is a Conditional Statement?

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A conditional statement is an 'if-then' statement that expresses a relationship between two propositions.

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What is a Biconditional Statement?

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A biconditional statement is a statement that combines a conditional statement and its converse, expressed as 'p if and only if q'.