Conditional & Biconditional Statements

Front

What is a biconditional statement?

Back

A biconditional statement is a statement that combines a conditional statement and its converse, expressed as 'P if and only if Q'. It is true when both the original statement and its converse are true.

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 the converse of a conditional statement?

Back

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

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'.

Front

When is a biconditional statement true?

Back

A biconditional statement is true when both the original conditional statement and its converse are true.

Front

What is an example of a biconditional statement?

Back

An example of a biconditional statement is: 'An angle is a right angle if and only if its measure is 90 degrees'.

Front

What does it mean if a statement is a conjecture?

Back

A conjecture is a statement that is believed to be true based on observations but has not yet been proven.

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.

Front

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

Back

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