Conditional Statements & Related Conditionals

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What is a conditional statement?

Back

A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). For example, 'If it rains, then the ground is wet.'

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P.' It is logically equivalent to the original statement.

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What is the converse of a conditional statement?

Back

The converse of a conditional statement 'If P, then Q' is 'If Q, then P.' It is not necessarily logically equivalent to the original statement.

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What is the inverse of a conditional statement?

Back

The inverse of a conditional statement 'If P, then Q' is 'If not P, then not Q.' It is not necessarily logically equivalent to the original statement.

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What is an acute angle?

Back

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

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What is a triangle with 3 congruent sides called?

Back

A triangle with 3 congruent sides is called an equilateral triangle.

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What is the truth value of a conditional statement?

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The truth value of a conditional statement indicates whether the statement is true or false based on the truth of its hypothesis and conclusion.

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Provide an example of a counterexample for a conditional statement.

Back

For the statement 'If an angle is acute, then it measures 30 degrees,' a counterexample is an angle measuring 20 degrees, which is acute but does not measure 30 degrees.

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What does it mean if a conditional statement is false?

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A conditional statement is false if the hypothesis is true and the conclusion is false.

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What is the relationship between a conditional statement and its contrapositive?

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A conditional statement and its contrapositive are logically equivalent; if one is true, the other is also true.