Laws of Logic (Detachment and Syllogism)

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What is the Law of Syllogism?

Back

The Law of Syllogism states that if 'p implies q' and 'q implies r', then 'p implies r'. It allows for drawing conclusions from two conditional statements.

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What is the Law of Detachment?

Back

The Law of Detachment states that if 'p implies q' is true and 'p' is true, then 'q' must also be true.

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What is a conditional statement?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, typically written as 'if p, then q'.

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What is the contrapositive of a statement?

Back

The contrapositive of a statement 'if p, then q' is 'if not q, then not p'. It is logically equivalent to the original statement.

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What is the converse of a statement?

Back

The converse of a statement 'if p, then q' is 'if q, then p'. It is not necessarily logically equivalent to the original statement.

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Provide an example of the Law of Syllogism.

Back

If it rains, then the ground is wet. If the ground is wet, then the grass is wet. Therefore, if it rains, then the grass is wet.

Front

Provide an example of the Law of Detachment.

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If I study, then I will pass the test. I studied. Therefore, I will pass the test.

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What is the conclusion of the statement: If a number is odd, then it is not even. The number is not even.

Back

Then the number is odd.

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What is the difference between a valid argument and a sound argument?

Back

A valid argument is one where if the premises are true, the conclusion must be true. A sound argument is a valid argument with true premises.

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What does it mean for a statement to be logically equivalent?

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Two statements are logically equivalent if they have the same truth value in every possible scenario.