Conditional and Biconditional 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.

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What is a biconditional statement?

Back

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

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'.

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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

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 a counterexample?

Back

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

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; it is true in all other cases.

Front

What is the relationship between a statement and its contrapositive?

Back

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

Front

What is the relationship between a statement and its inverse?

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A conditional statement and its inverse are not logically equivalent; one can be true while the other is false.

Front

What is the relationship between a statement and its converse?

Back

A conditional statement and its converse are not logically equivalent; one can be true while the other is false.