Conditional 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.

Front

What is the inverse of a conditional statement p→q?

Back

The inverse is ∼p→∼q.

Front

What is the contrapositive of a conditional statement p→q?

Back

The contrapositive is ∼q→∼p.

Front

What does the symbol ~ represent in logic?

Back

The symbol ~ represents negation, meaning 'not'.

Front

If p is true and q is false, what is the truth value of the conditional statement p→q?

Back

The truth value is false.

Front

What is the converse of a conditional statement p→q?

Back

The converse is q→p.

Front

Given the 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

What is the difference between a conditional statement and its converse?

Back

A conditional statement has the form 'If p, then q', while the converse has the form 'If q, then p'.

Front

What is an example of a conditional statement?

Back

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

Front

What is the truth table for a conditional statement?

Back

The truth table has four combinations: TT (True), TF (False), FT (True), FF (False). The only false case is when p is true and q is false.