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'.

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What is the converse of a conditional statement?

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The converse of a conditional statement 'If P, then Q' is 'If Q, then P'. It switches the hypothesis and conclusion.

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'. It negates both the hypothesis and conclusion and switches them.

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 the hypothesis and conclusion.

Front

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

Back

Hypothesis: It rains; Conclusion: The ground is wet.

Front

What is the logical form of a conditional statement?

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The logical form of a conditional statement is represented as P → Q, where P is the hypothesis and Q is the conclusion.

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How do you determine the truth value of a conditional statement?

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A conditional statement is false only when the hypothesis is true and the conclusion is false. In all other cases, it is true.

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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 converse of the statement: 'If a number is even, then it is divisible by 2'?

Back

If a number is divisible by 2, then it is even.

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What is the contrapositive of the statement: 'If a student studies, then they will pass the exam'?

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If a student does not pass the exam, then they did not study.