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Translating Quantified Statements Into English

  1. Feb 3, 2013 #1
    1. The problem statement, all variables and given/known data
    Translate these statements into English, where C(x) is “x is a comedian” and F(x) is “x is funny” and the domain consists of all people.

    a) ∀x(C(x)→F(x))

    b)∀x(C(x)∧F(x))

    c) ∃x(C(x)→F(x))

    d)∃x(C(x)∧F(x))


    2. Relevant equations



    3. The attempt at a solution

    Here are my answers:

    For a): For every person, if they are a comedian, then they are funny.

    For b): For every person, they are both a comedian and funny.

    For c): There exists a person who, if he is funny, is a comedian

    For d): There exists a person who is funny and is a comedian.

    Here are the books answers:

    a)Every comedian is funny.
    b)Every person is a funny comedian.
    c)There exists a person such that if she or he is a comedian, then she or he is funny.
    d)Some comedians are funny.


    Does the meaning of my answers seem to be in harmony with the meaning of the answers given in the solution manual?
     
  2. jcsd
  3. Feb 4, 2013 #2
    The reason I ask is because part a), for instance, is a implication, and "Every comedian is funny," does not appear to be an implication.
     
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