Reasoning and Proof

Front

What is reasoning in mathematics?

Back

Reasoning in mathematics refers to the process of thinking logically about mathematical concepts and relationships to draw conclusions or make inferences.

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Define proof in mathematics.

Back

A proof is a logical argument that establishes the truth of a mathematical statement based on previously accepted statements, such as axioms and theorems.

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What is a conjecture?

Back

A conjecture is a statement that is believed to be true based on observations but has not yet been proven.

Front

What is the difference between inductive and deductive reasoning?

Back

Inductive reasoning involves making generalizations based on specific examples, while deductive reasoning involves applying general principles to reach specific conclusions.

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What is the Law of Syllogism?

Back

The Law of Syllogism states that if 'p implies q' and 'q implies r', then 'p implies r'.

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What is a counterexample?

Back

A counterexample is an example that disproves a conjecture or statement.

Front

What does it mean for two angles to be complementary?

Back

Two angles are complementary if the sum of their measures is 90 degrees.

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What is the definition of an acute angle?

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An acute angle is an angle that measures less than 90 degrees.

Front

What is the Symmetric Property of Equality?

Back

The Symmetric Property of Equality states that if a = b, then b = a.

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What is the Transitive Property of Equality?

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The Transitive Property of Equality states that if a = b and b = c, then a = c.