Converse, Inverse, Contrapositive

Front

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.'

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'. For example, the converse of 'If it rains, then the ground is wet' is 'If the ground is wet, then it rains.'

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'. For example, the inverse of 'If it rains, then the ground is wet' is 'If it does not rain, then the ground is not wet.'

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'. For example, the contrapositive of 'If it rains, then the ground is wet' is 'If the ground is not wet, then it does not rain.'

Front

Given the statement 'If I am hungry, then I eat', what is the inverse?

Back

If I am not hungry, then I don't eat.

Front

Given the statement 'If an angle is obtuse, then it is greater than 90 degrees', what is the contrapositive?

Back

If an angle is not greater than 90 degrees, then it is not obtuse.

Front

What does it mean if a conclusion is valid?

Back

A conclusion is valid if it logically follows from the premises or statements given.

Front

What is the difference between a converse and an inverse?

Back

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

Front

If Jenny buys a guitar, then she will not buy a keyboard. What is the contrapositive?

Back

If Jenny buys a keyboard, then she will not buy a guitar.

Front

What is an example of a conditional statement?

Back

If it is sunny, then we will go to the park.