Logic Laws and Logic Review

Front

What is the Law of Contrapositive?

Back

The Law of Contrapositive states that if a conditional statement is true, then its contrapositive is also true. The contrapositive of 'If P, then Q' is 'If not Q, then not P.'

Front

Provide an example of the Law of Contrapositive.

Back

If the statement is 'If the airport is crowded, then I will miss my flight,' the contrapositive is 'If I did not miss my flight, then the airport was not crowded.'

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What is the Law of Detachment?

Back

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then the conclusion must also be true.

Front

Provide an example of the Law of Detachment.

Back

If the statement is 'If a plane flies to China, then it will be a long flight,' and Sarah bought a ticket to China, we can conclude 'Sarah will have a long flight.'

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What is a hypothesis in a conditional statement?

Back

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

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What is a conclusion in a conditional statement?

Back

The conclusion is the part of a conditional statement that follows 'then.' It represents the result or outcome of the hypothesis being true.

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What is the Law of Syllogism?

Back

The Law of Syllogism states that if 'If P, then Q' and 'If Q, then R' are both true, then 'If P, then R' is also true.

Front

Provide an example of the Law of Syllogism.

Back

If the statements are 'If you study, then you will pass the test' and 'If you pass the test, then you will pass the class,' we can conclude 'If you study, then you will pass the class.'

Front

What is a contrapositive?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P.' It is logically equivalent to the original statement.

Front

Provide an example of a contrapositive.

Back

For the statement 'If a polygon is a quadrilateral, then it is a trapezoid,' the contrapositive is 'If a polygon is not a trapezoid, then it is not a quadrilateral.'