Logical Reasoning in Geometry

If Teri goes to the beach then she will collect shells.

Identify the hypothesis

What is the core principle of the Law of Detachment?

• If the conclusion of a conditional statement is true, then the hypothesis is true.

• If the hypothesis of a conditional statement is true, then the conclusion is true.

• If two conditional statements have the same conclusion, then their hypotheses are related.

• If two conditional statements have the same hypothesis, then their conclusions are related.

Given the statement "If there is lightning, then it is not safe to be outside," and the observation that "Preston sees lightning from the baseball field," what can be concluded?

• Preston should continue playing baseball.

• It is not safe for Preston to be outside.

• Preston should look for lions or aliens.

• The lightning is not dangerous.

If the statement "If there is lightning, then it is not safe to be outside" is true, and we know "It is not safe for Preston to be outside," can we conclude that there is lightning?

• Yes, because the unsafe condition must be due to lightning.

• No, because there could be other reasons why it's not safe.

• Yes, this is an application of the Law of Detachment.

• No, because the Law of Detachment only applies when the conclusion is false.

What is the correct conclusion based on the Law of Syllogism for the following statements: "If everyone does their Geometry homework, then they will pass Geometry." and "If everyone passes Geometry, then Mrs. Gray will have a party!"

• If everyone passes Geometry, then everyone does their Geometry homework.

• If everyone does their Geometry homework, then Mrs. Gray will have a party!

• If Mrs. Gray has a party, then everyone passed Geometry.

• Everyone will pass Geometry and Mrs. Gray will have a party.

Given: If two lines are parallel, then they never intersect.

Given: If two lines never intersect, then they have the same slope.

Conclusion: If two lines are parallel, then they have the same slope.

• Invalid

• Law of Detachment

• Law of Syllogism

• Law of Lilynism

Given: If you are at least 18 years old, then you can apply for a credit card.

Given: Kelly applied for a credit card.

Conclusion: Kelly is at least 18 years old.

• Invalid

• Law of detachment

• Law of Syllogism

• Law of lilyism