Law of Detachment & Law of Syllogism

Multiple Choice

Which represents the Law of Detachment?

• If $$p\rightarrow q$$ is true and $$q$$ is true, then $$p$$  is true

• If $$q\rightarrow p$$ is true and $$p$$ is true, then $$q$$  is true

• If $$p\rightarrow q$$ is true and $$p$$ is true, then $$q$$  is true

• If $$p\rightarrow q$$  is true and $$q\rightarrow r$$  is true, then $$p\rightarrow r$$ is true

Multiple Choice

Which represents the Law of Syllogism?

• If $$p\rightarrow q$$ is true and $$p$$ is true, then $$q$$  is true

• If $$q\rightarrow p$$ is true and $$r\rightarrow p$$ is true, then $$q\rightarrow r$$  is true

• If $$p\rightarrow q$$ is true and $$p\rightarrow r$$ is true, then $$p\rightarrow q$$  is true

• If $$p\rightarrow q$$  is true and $$q\rightarrow r$$  is true, then $$p\rightarrow r$$ is true

Multiple Choice

Determine if the following statement is true or false and which law is applicable:

GIVEN: If the sum of the measures of 2 angles is 180, then the angles are supplementary.

m<A + m<B =180.

CONCLUSION: <A and <B are supplementary.

• True by Law of Detachment

• True by Law of Syllogism

• False

Multiple Choice

Determine if the following statement is true or false and which law is applicable:

GIVEN: If it is Tuesday, then Anna tutors her friend in Biology. If Anna tutors her friend in Biology, then she gets Starbucks afterwards.

CONCLUSION: Anna got Starbucks on Tuesday.

• True by Law of Detachment

• True by Law of Syllogism

• False

Multiple Choice

Determine if the following statement is true or false and which law is applicable:

GIVEN: If the heat wave continues, then air conditioning will be used more frequently. If air conditioning is used more frequently, then energy costs will be higher.

CONCLUSION: If the heat wave continues, then energy costs will be higher.

• True by Law of Detachment

• True by Law of Syllogism

• False

Multiple Choice

Determine if the following statement is true or false and which law is applicable:

GIVEN: If a marine animal is a starfish, then it lives in the intertidal zone of the ocean. If a marine animal lives in the intertidal zone of the ocean, then it can be must be able to survive if it exposed to air.

CONCLUSION: The intertidal zone is the least stable of the ocean zones.

• True by Law of Detachment

• True by Law of Syllogism

• F

Multiple Choice

Determine if the following statement is true or false and which law is applicable:

GIVEN: If it is Monday, then Penny has dance class after school. Penny had dance.

CONCLUSION: It is Monday.

• True by Law of Detachment

• True by Law of Syllogism

• False

Multiple Choice

If I like my math class, then I will earn an "A". I like my Geometry class.

• I will earn an "A".

• I will not like my math class.

• I will not earn an "A".

• no valid conclusion

Multiple Choice

If it is raining, then I use an umbrella. I am using my umbrella.

• It is raining.

• It is not raining.

• It is hot outside.

• no valid conclusion

Multiple Choice

If the football team wins on Friday night, then practice is canceled for Monday.

The football team won by 7 points on Friday night.

• Practice is canceled for Monday.

• The football team will have practice.

• 7 points is not enough of a margin of winning.

• no valid conclusion

Multiple Choice

If you go to the movies, then you'll eat popcorn.

If you eat popcorn, then you'll enjoy the movie.

• If you eat popcorn, then you went to the movies.

• if you go to the movie, then you'll enjoy the movie.

• If you enjoyed the movie, then you ate popcorn.

• no valid conclusion

Multiple Choice

If it is raining, the temperature is greater than 32 degrees.

If the temperature is greater than 32 degrees, then it is not freezing outside.

• If it is freezing outside, then it is less than 32 degrees outside.

• If it is raining, then it is not freezing outside.

• If it is greater than 32 degrees outside, then it is raining.

• no valid conclusion

Multiple Choice

If you miss the bus, then you'll be late for school.

Jacob was late for school.

• Jacob missed the bus.

• Jacob slept through his alarm.

• Jacob's mom drove him to school.

• no valid conclusion

Multiple Choice

If a person is a librarian, then they read books.

If a person reads books, then they are smart.

• Dana is a librarian, so Dana reads books.

• If a person is smart, then they read books.

• If a person is a librarian, then they are smart.

• no valid conclusion