Related Conditionals

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). It is often written in the form 'If P, then 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', denoted as @@ eg Q ightarrow eg 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', denoted as @@ eg P ightarrow eg 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', denoted as @@ Q ightarrow P @@.

Front

How do you form the contrapositive of the statement: 'If you play the guitar, then you are a musician'?

Back

The contrapositive is: 'If you are not a musician, then you do not play the guitar'.

Front

How do you form the inverse of the statement: 'If you are 13, then you are a teenager'?

Back

The inverse is: 'If you are not 13, then you are not a teenager'.

Front

What is the relationship between a statement and its contrapositive?

Back

A 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?

Back

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

Front

What is the relationship between a statement and its converse?

Back

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

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'.