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Thread: Discrete maths proofs

  1. #1
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    Discrete maths proofs

    1. A\(B\C) = (A\B) U (A \C)
    Can someone help me to prove this ? :/
    Last edited by juliusxxc; Mar 25th 2018 at 11:23 AM.
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  2. #2
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    Re: Discrete maths proofs

    Unfortunately, you have not given us any indication of what level of mathematics you have had exposure to. I recommend taking a stab at it, showing us your work and where you are stuck, and then we can help you. Are you familiar with set complements? What theorems have you already proven?
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  3. #3
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    Re: Discrete maths proofs

    Quote Originally Posted by juliusxxc View Post
    1. A\(B\C) = (A\B) U (A \C)
    Can someone help me to prove this ? :/
    @juliusxxc, I absolutely agree with others that you must show some effort.

    Suppose that $A=\{a,b,c,d,e,f\}~,~B=\{a,d,e,f\}~,\&~C=\{a,e\}$

    Now you show us:
    $A\setminus B=?$ , $A\setminus C=?$ , & $B\setminus C=?$

    So $A\setminus (B\setminus C)=?$
    Last edited by Plato; Mar 25th 2018 at 03:08 PM.
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  4. #4
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    Re: Discrete maths proofs

    A\B = {b, c, d} A\C = {b, c, d, f} B\C = {d, f}
    A\(B\C) = {a, b, c, e}
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  5. #5
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    Re: Discrete maths proofs

    Sorry for the first post,
    I am trying to do my discrete maths HW, and there is 2 exc left.
    I need to show proofs from both sides.
    First one:
    Discrete maths proofs-30226255_2394303197261973_1134567876695425024_o.jpg

    Second:
    Discrete maths proofs-29793558_2394303233928636_5669303482931216384_o.jpg

    And i can only use definitions and bullian algebra:
    Discrete maths proofs-29793487_2394303223928637_4277914806956064768_o.jpg

    this is an example how we do things:
    Discrete maths proofs-30127174_2394327817259511_6131991088434511872_o.jpg
    Ir - mean n, ARBA means u.
    I dont have enough examples to prove this :/
    Last edited by juliusxxc; Apr 6th 2018 at 04:21 AM.
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  6. #6
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    Re: Discrete maths proofs

    Quote Originally Posted by juliusxxc View Post
    A\B = {b, c, d}
    No, that's wrong. There is a "d" in B so there is no "d" in A\B. A\B= {b, c}.

    A\C = {b, c, d, f} B\C = {d, f}
    A\(B\C) = {a, b, c, e}
    Yes, those are correct. And (A\B)U(A\C)= {b,c}U{b, c, d, f}= {b, c, d, f} which is NOT the same as A/(B\C).

    Plato's point was that you can't prove this "theorem", it is NOT true!
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  7. #7
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    Re: Discrete maths proofs

    well i still need to show it in the way that i showed you bellow.
    Thanks for taking time and replying
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  8. #8
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    Re: Discrete maths proofs

    Quote Originally Posted by juliusxxc View Post
    well i still need to show it in the way that i showed you bellow.
    You are wasting your time as well as our time.
    You cannot prove something true if it is false.
    The example I posted shows that $A\setminus (B\setminus C)\ne (A\setminus B)\cup(A\setminus C)$ in general.
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  9. #9
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    Re: Discrete maths proofs

    You could prove

    $$A\setminus (B \setminus C) = (A\setminus B) \cup (A \cap C)$$

    $$\begin{align*}A\setminus (B\setminus C) & = A \setminus (B \cap C^c) \\ & = A \cap (B\cap C^c)^c \\ & = A\cap (B^c \cup C) \\ & = (A \cap B^c) \cup (A \cap C) \\ & = (A \setminus B) \cup (A \cap C)\end{align*}$$
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  10. #10
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    Re: Discrete maths proofs

    Quote Originally Posted by juliusxxc View Post
    Could you explain what does the little c means ?
    That's the complement of a set

    $A^c = \{x : x \not \in A\}$
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