Conditional Statements & 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 truth value of a conditional statement?

Back

The truth value of a conditional statement is true unless the hypothesis is true and the conclusion is false.

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'. It is logically equivalent to the original statement.

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'. It is not necessarily logically equivalent to the original statement.

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'. It is also not necessarily logically equivalent to the original statement.

Front

Example of a conditional statement: 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

Example of a conditional statement: If a shape is a square, then it has four sides. What is the converse?

Back

If a shape has four sides, then it is a square.

Front

Example of a conditional statement: If a number is even, then it is divisible by 2. What is the inverse?

Back

If a number is not even, then it is not divisible by 2.

Front

What is an acute angle?

Back

An acute angle is an angle that measures less than 90 degrees.

Front

What is an equilateral triangle?

Back

An equilateral triangle is a triangle in which all three sides are of equal length.