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

Fill in the Blanks

If a tennis player is good, they are quick. Martina is a good tennis player.

Fill in the Blanks

If I don’t wear sunscreen while swimming, then I’ll get sunburned.

If I get sunburned, then I’ll be in pain.

Fill in the Blanks

If it is sunny, then I wear flip flops. I have on flip flops.

Fill in the Blanks

If a polygon is regular, then all sides and all angles are congruent.

If all sides and all angles are congruent, then the polygon is convex.

Fill in the Blanks

If my kids are sleepy, then they are cranky.

If my kids are sleepy, then they get in fights.

Fill in the Blanks

If there is more than 12 inches of snow, then we will have a snow day.

If we have a snow day, then we watch movies all day.