Logic Syllogism & Detachment Flashcards
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Questions and Answers

If Jon studied for his test, what conclusion can we draw based on the Law of Detachment?

  • Jon studied too hard.
  • Jon will fail his test.
  • Jon will be unhappy.
  • Jon will pass his test. (correct)

    • If Cierra's car ran out of gas, what can we conclude?

  • Cierra will be late.
  • Cierra will walk.
  • Cierra will call for help.
  • Cierra's car won't start. (correct)

    • According to the Law of Detachment, what conclusion follows from Jake enjoying the complexity of math?

  • Jake will fail his math test.
  • Jake will become famous.
  • Jake dislikes math.
  • Jake is a mathematician. (correct)

    • What conclusion can we draw from Sam being happy if it is stated that if you pass your test, then you will be happy?

    <p>No conclusion</p> Signup and view all the answers

    What conclusion can we draw from Chelsea eating cake if it is stated that if it is your birthday, then you will eat cake?

    <p>No conclusion</p> Signup and view all the answers

    What can be concluded if I save my money?

    <p>I will attend the basketball game.</p> Signup and view all the answers

    Based on the Law of Syllogism, what conclusion can we draw from owning a Labradoodle and having a dog?

    <p>You are a pet owner.</p> Signup and view all the answers

    What conclusion can we draw about getting dirty if you fall in the mud and you take a shower?

    <p>No conclusion</p> Signup and view all the answers

    If two angles are vertical, what can be concluded about their measures according to the Law of Syllogism?

    <p>They are congruent.</p> Signup and view all the answers

    If I use an umbrella, what conclusion can be drawn?

    <p>I won't get wet.</p> Signup and view all the answers

    What follows if James drove over the speed limit?

    <p>James got a ticket.</p> Signup and view all the answers

    What conclusion can be drawn about Ryan's health?

    <p>Ryan is in good health.</p> Signup and view all the answers

    What conclusion can we draw from Jenny being late for school?

    <p>No conclusion</p> Signup and view all the answers

    What conclusion can we draw from the fact that angle A and angle B are congruent?

    <p>No conclusion</p> Signup and view all the answers

    If you go swimming, what is implied?

    <p>It is summer.</p> Signup and view all the answers

    If you are learning about angle relationships, what can be concluded?

    <p>You are in a math class.</p> Signup and view all the answers

    If Cameron is a football player, what conclusion can we reach?

    <p>Cameron is an athlete.</p> Signup and view all the answers

    What conclusion follows from the fact that the city of Philadelphia is celebrating?

    <p>No conclusion</p> Signup and view all the answers

    If you are 14 years old, what can we conclude regarding your ability to drive?

    <p>You cannot drive a car.</p> Signup and view all the answers

    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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    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!

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