Law of Detachment and Syllogism

Front

What is the Law of Detachment?

Back

The Law of Detachment states that if a conditional statement (p → q) is true and the hypothesis (p) is true, then the conclusion (q) must also be true.

Front

Provide an example of the Law of Detachment.

Back

If it is raining (p), then the ground is wet (q). It is raining (p). Therefore, the ground is wet (q).

Front

What is the Law of Syllogism?

Back

The Law of Syllogism states that if the first statement implies a second statement (p → q) and the second statement implies a third statement (q → r), then the first statement implies the third statement (p → r).

Front

Provide an example of the Law of Syllogism.

Back

If it is snowing (p), then school is canceled (q). If school is canceled (q), then the big test will not be given today (r). Therefore, if it is snowing (p), then the big test will not be given today (r).

Front

What does it mean if a conclusion is 'invalid'?

Back

A conclusion is considered 'invalid' if it does not logically follow from the premises or statements provided.

Tags

CCSS.RI.7.8

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.8.1

CCSS.RL.9-10.1

Front

How can you determine if a conclusion is valid using the Law of Detachment?

Back

To determine if a conclusion is valid using the Law of Detachment, check if the hypothesis of the conditional statement is true. If it is, then the conclusion must also be true.

Front

What is a conditional statement?

Back

A conditional statement is a logical statement that has two parts: a hypothesis (p) and a conclusion (q), typically expressed in the form 'If p, then q'.

Front

What is the significance of the hypothesis in a conditional statement?

Back

The hypothesis is the condition that must be met for the conclusion to be true. If the hypothesis is false, the truth of the conclusion cannot be determined.

Front

What is a counterexample in the context of logical statements?

Back

A counterexample is an example that disproves a statement or proposition by showing that the conclusion does not hold true when the hypothesis is true.

Front

How do you apply the Law of Syllogism in problem-solving?

Back

To apply the Law of Syllogism, identify two conditional statements where the conclusion of the first statement matches the hypothesis of the second statement, then derive a new conclusion.