Conditional and Biconditional Statements

Front

What is a conditional statement?

Back

A conditional statement is a logical statement that has the form 'If P, then Q', where P is the hypothesis and Q is the conclusion.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

Front

What is a converse statement?

Back

The converse of a conditional statement 'If P, then Q' is 'If Q, then P'.

Front

What is a biconditional statement?

Back

A biconditional statement is a logical statement that combines a conditional and its converse, expressed as 'P if and only if Q'.

Front

What is a contrapositive statement?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'.

Front

What is an inverse statement?

Back

The inverse of a conditional statement 'If P, then Q' is 'If not P, then not Q'.

Front

How do you form the converse of the statement: 'If a polygon is a quadrilateral, then it is a trapezoid'?

Back

The converse is: 'If a polygon is a trapezoid, then it is a quadrilateral.'

Front

How do you form the contrapositive of the statement: 'If a polygon is a quadrilateral, then it is a trapezoid'?

Back

The contrapositive is: 'If a polygon is not a trapezoid, then it is not a quadrilateral.'

Front

How do you form the inverse of the statement: 'If a polygon is a quadrilateral, then it is a trapezoid'?

Back

The inverse is: 'If a polygon is not a quadrilateral, then it is not a trapezoid.'

Front

What is the biconditional for the statement: 'A right angle is an angle with 90 degrees'?

Back

The biconditional is: 'An angle is a right angle if and only if it has 90 degrees.'

Front

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

Back

A conditional statement and its contrapositive are logically equivalent; if one is true, the other is also true.