Conditional statements

Front

What is a conditional statement?

Back

A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). It is often written in the form 'If P, then Q'.

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

Write the statement 'If it rains, then the ground is wet' in if-then form.

Back

If it rains, then the ground is wet.

Front

Identify the hypothesis and conclusion in the statement: 'If a student studies, then they will pass the exam.'

Back

Hypothesis: A student studies; Conclusion: They will pass the exam.

Front

What is the relationship between a statement and its contrapositive?

Back

A statement and its contrapositive are logically equivalent, meaning they have the same truth value.

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What is the relationship between a statement and its converse?

Back

A statement and its converse are not necessarily logically equivalent; they can have different truth values.

Front

Provide an example of a conditional statement and its converse.

Back

Conditional: If a shape is a square, then it has four sides. Converse: If a shape has four sides, then it is a square.

Front

What does it mean for a conditional statement to be true?

Back

A conditional statement is true unless the hypothesis is true and the conclusion is false.