Geometry - Conditional Statements

Front

What is a conditional statement?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, where the first proposition (hypothesis) implies the second proposition (conclusion).

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', meaning both p and q are true or both are false.

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 switches the hypothesis and conclusion.

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 negates both the hypothesis and conclusion.

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 switches and negates both the hypothesis and conclusion.

Front

When is a conditional statement false?

Back

A conditional statement is false only when the hypothesis is true and the conclusion is false.

Front

What does it mean for two statements to be logically equivalent?

Back

Two statements are logically equivalent if they have the same truth value in all possible scenarios.

Front

What is a hypothesis in a conditional statement?

Back

The hypothesis is the part of a conditional statement that follows 'if'. It is the condition that must be satisfied.

Front

What is a conclusion in a conditional statement?

Back

The conclusion is the part of a conditional statement that follows 'then'. It is the result that follows from the hypothesis.

Front

What is an example of a biconditional statement?

Back

An example of a biconditional statement is 'A figure is a square if and only if it is a rectangle with equal sides.'