Conditional and Biconditional Statements

Front

What is a Conditional Statement?

Back

A statement that can be written in the form 'If p, then q', where p is the hypothesis and q is the conclusion.

Front

What does the symbol ~p represent?

Back

The negation of statement p, meaning 'not p'.

Front

What is the Inverse Statement of 'If p, then q'?

Back

The Inverse Statement is 'If not p, then not q'.

Front

What is the Converse Statement of 'If p, then q'?

Back

The Converse Statement is 'If q, then p'.

Front

What is the Contrapositive Statement of 'If p, then q'?

Back

The Contrapositive Statement is 'If not q, then not p'.

Front

Identify the hypothesis in the statement: 'If it rains, then the ground is wet.'

Back

The hypothesis is 'It rains'.

Front

Identify the conclusion in the statement: 'If it rains, then the ground is wet.'

Back

The conclusion is 'The ground is wet'.

Front

What does it mean to negate a statement?

Back

To negate a statement means to state the opposite of that statement.

Front

What is the relationship between a Conditional Statement and its Contrapositive?

Back

A Conditional Statement and its Contrapositive are logically equivalent; they have the same truth value.

Front

What is the truth value of a Conditional Statement when the hypothesis is false?

Back

The truth value is always true, regardless of the conclusion.