Conditional Statements

Front

What is a conditional statement?

Back

A conditional statement is a logical statement that has the form 'If P, then Q', where P is the hypothesis and Q is the conclusion.

Front

What is a biconditional statement?

Back

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

Front

What is the converse of a conditional statement?

Back

The converse of a conditional statement 'If P, then Q' is 'If Q, then P'.

Front

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'.

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'.

Front

How do you determine the truth value of a conditional statement?

Back

A conditional statement is false only when the hypothesis is true and the conclusion is false; otherwise, it is true.

Front

What is an example of a biconditional statement?

Back

An example of a biconditional statement is: 'An angle is acute if and only if its measure is less than 90°.'

Front

What is the relationship between a statement and its contrapositive?

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A statement and its contrapositive are logically equivalent; they have the same truth value.

Front

What is the difference between a converse and an inverse?

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The converse switches the hypothesis and conclusion, while the inverse negates both the hypothesis and conclusion.

Front

Provide an example of a conditional statement.

Back

If it rains, then the ground will be wet.