Questions and Answers
If Jon studied for his test, what conclusion can we draw based on the Law of Detachment?
If Cierra's car ran out of gas, what can we conclude?
According to the Law of Detachment, what conclusion follows from Jake enjoying the complexity of math?
What conclusion can we draw from Sam being happy if it is stated that if you pass your test, then you will be happy?
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What conclusion can we draw from Chelsea eating cake if it is stated that if it is your birthday, then you will eat cake?
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What can be concluded if I save my money?
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Based on the Law of Syllogism, what conclusion can we draw from owning a Labradoodle and having a dog?
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What conclusion can we draw about getting dirty if you fall in the mud and you take a shower?
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If two angles are vertical, what can be concluded about their measures according to the Law of Syllogism?
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If I use an umbrella, what conclusion can be drawn?
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What follows if James drove over the speed limit?
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What conclusion can be drawn about Ryan's health?
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What conclusion can we draw from Jenny being late for school?
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What conclusion can we draw from the fact that angle A and angle B are congruent?
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If you go swimming, what is implied?
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If you are learning about angle relationships, what can be concluded?
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If Cameron is a football player, what conclusion can we reach?
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What conclusion follows from the fact that the city of Philadelphia is celebrating?
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If you are 14 years old, what can we conclude regarding your ability to drive?
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Study Notes
Law of Detachment
- Applies when a conditional statement is true and the hypothesis is affirmed.
- If you study for your test, then you will pass; Jon studied, so Jon will pass.
- If your car runs out of gas, then your car won't start; Cierra's car ran out of gas, so it won't start.
- If you enjoy the complexity of math, you are a mathematician; Jake enjoys math, so he is a mathematician.
- If you drive over the speed limit, you will get a ticket; James drove over the limit, thus he got a ticket.
- If you exercise regularly, you will be in good health; Ryan exercises regularly, so he is in good health.
- No conclusions can be drawn when only the consequence is known, such as Sam being happy or Chelsea eating cake.
Law of Syllogism
- Used when two conditional statements share a common term.
- If I save my money, I can buy tickets; if I buy tickets, I will attend the game; therefore, if I save money, I will attend the game.
- If you own a Labradoodle, you have a dog; if you have a dog, you are a pet owner; thus, owning a Labradoodle means you are a pet owner.
- If two angles are vertical, then they are congruent; if they are congruent, they have the same measure; therefore, vertical angles have the same measure.
- If you go swimming, it is summer; if you are at the pool, you go swimming; hence, if you are at the pool, it is summer.
- If you take geometry, you are in a math class; if you learn about angle relationships, you take geometry; therefore, learning about angles means you are in a math class.
- If you are a football player, you are an athlete; Cameron is a football player; hence, he is an athlete.
Situations with No Conclusions
- Certain scenarios lead to no definitive conclusions based on the provided information.
- Sam being happy does not confirm he passed the test.
- Chelsea eating cake doesn't necessarily indicate it is her birthday.
- Jenny being late for school doesn't allow for a conclusion about missing the bus.
- Angle A and Angle B being congruent doesn’t confirm any additional relationships without further information.
- The celebration in Philadelphia does not provide information about the football team's victory in the Super Bowl.
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Description
Test your understanding of the laws of syllogism and detachment with these flashcards. Each card presents a scenario using logical reasoning to identify conclusions based on given premises. Perfect for students looking to improve their critical thinking skills!
