Converse, Inverse, Contrapositive

Front

What is the converse of a statement?

Back

The converse of a statement is formed by reversing the hypothesis and conclusion. For example, the converse of 'If it is night, then it is dark outside' is 'If it is dark outside, then it is night.'

Front

What is the inverse of a statement?

Back

The inverse of a statement is formed by negating both the hypothesis and conclusion. For example, the inverse of 'If it is night, then it is dark outside' is 'If it is not night, then it is not dark outside.'

Front

What is the contrapositive of a statement?

Back

The contrapositive of a statement is formed by reversing and negating both the hypothesis and conclusion. For example, the contrapositive of 'If it is night, then it is dark outside' is 'If it is not dark outside, then it is not night.'

Front

What is an example of a conditional statement?

Back

An example of a conditional statement is 'If it rains, then the ground will be wet.'

Front

How do you identify the hypothesis in a conditional statement?

Back

The hypothesis is the part of the statement that follows 'if.' In 'If it rains, then the ground will be wet,' the hypothesis is 'it rains.'

Front

How do you identify the conclusion in a conditional statement?

Back

The conclusion is the part of the statement that follows 'then.' In 'If it rains, then the ground will be wet,' the conclusion is 'the ground will be wet.'

Front

What is the relationship between a statement and its contrapositive?

Back

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

Front

What is the relationship between a statement and its converse?

Back

A statement and its converse are not necessarily logically equivalent; they can have different truth values.

Front

What is the relationship between a statement and its inverse?

Back

A statement and its inverse are not necessarily logically equivalent; they can have different truth values.

Front

If the statement is 'If A, then B,' what is the converse?

Back

The converse is 'If B, then A.'