Conditional, Converse, Inverse, Contrapositive Biconditional

Front

What is a conditional statement?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, where one proposition (the hypothesis) implies the other (the conclusion).

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

What is a biconditional statement?

Back

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

Front

If the statement is 'If it rains, then the ground is wet', what is the contrapositive?

Back

If the ground is not wet, then it does not rain.

Front

If the statement is 'If I study, then I will pass the test', what is the inverse?

Back

If I do not study, then I will not pass the test.

Front

What does the contrapositive of a statement tell us?

Back

The contrapositive of a statement is logically equivalent to the original statement, meaning if one is true, the other is also true.

Front

If the statement is 'If I am tired, then I will sleep', what is the converse?

Back

If I sleep, then I am tired.

Front

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

Back

A conditional statement and its contrapositive are logically equivalent.