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Math Help - Finite Math help please multiple choice @

  1. #1
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    Finite Math help please multiple choice @

    11. ( p∨q) ≡
    A) p→q
    B) p
    C) p∧q
    D) Contradiction (F)

    12) (p∨p) ≡

    A) p→q
    B) p
    C) p∧q
    D) Tautology T)

    13) p∨(p∧q) ≡

    A) p→q
    B) p
    C) p∧q
    D) Tautology (T)



    14. Blue ⊆ A
    a) True
    b) False

    15. Re d ∉ A
    a) True
    b)

    16. {Green,Blue,Yellow} ⊂ A
    a) True
    b( False

    17. A ⊆∅
    a) True
    b) False
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  2. #2
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    Re: Finite Math help please multiple choice @

    First, logic is usually considered a topic in discrete mathematics, so this belongs in the discrete math subforum. Second, please don't post more than two questions in one thread. Third, this site is not a homework service. You have to show your attempt at the solution or at least describe what your difficulty is.

    Do you know how to determine the truth value of a Boolean formula and what truth tables are? Two formulas are equivalent if they have the same truth tables. You should also familiarize yourself with basic Boolean equivalences, such as De Morgan's laws and the definition of → through ∨ and , in your textbook, lecture notes or other source.

    Quote Originally Posted by iBrute View Post
    14. Blue ⊆ A
    a) True
    b) False
    What are Blue and A here?
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  3. #3
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    Re: Finite Math help please multiple choice @

    A = Blue,{ Green,Indigo,Violet,Orange,Yellow}

    This is for 14-17 forgot to post it
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  4. #4
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    Re: Finite Math help please multiple choice @

    Quote Originally Posted by iBrute View Post
    A = Blue,{ Green,Indigo,Violet,Orange,Yellow}
    You probably mean A = {Blue, Green, Indigo, Violet, Orange, Yellow}. I will assume that the colors themselves are not sets and that they are distinct (e.g., Blue ≠ Green).

    Quote Originally Posted by iBrute View Post
    14. Blue ⊆ A
    a) True
    b) False
    This is false because under the assumptions above this is a type error. Only sets can occur on the left-hand side of ⊆.

    Quote Originally Posted by iBrute View Post
    15. Re d ∉ A
    a) True
    b)
    I agree.

    Quote Originally Posted by iBrute View Post
    16. {Green,Blue,Yellow} ⊂ A
    a) True
    b( False
    Does every element of {Green,Blue,Yellow} also belong to A? Also, is {Green,Blue,Yellow} different from A? The symbol ⊂ denotes the relation of being a proper subset, i.e., a subset that is not equal to the whole set. (However, some sources use ⊂ to denote any subset. You need to check the definition in your textbook.)

    Quote Originally Posted by iBrute View Post
    17. A ⊆∅
    a) True
    b) False
    Does every element of A belong to the empty set?
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