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Math Help - Math Proof A-(B∩C)=(A-B)∪(A-C).

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    Math Proof A-(B∩C)=(A-B)∪(A-C).

    I have no idea how to solve this. Any help would be appreciated! The statement is
    For any sets A, B, and C that are subsets of a universal set U, A-(B∩C)=(A-B)∪(A-C).
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    Re: Math Proof A-(B∩C)=(A-B)∪(A-C).

    Use following properties:
    X-Y=X∩Y'
    (X∩Y)'=X'∪Y'
    A-(B∩C)=A∩(B∩C)'=A∩(B'∪C')=(A∩B')∪(A∩C')=(A-B)∪(A-C)
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    Re: Math Proof A-(B∩C)=(A-B)∪(A-C).

    Quote Originally Posted by goalkeeper00 View Post
    I have no idea how to solve this. Any help would be appreciated! The statement is
    For any sets A, B, and C that are subsets of a universal set U, A-(B∩C)=(A-B)∪(A-C).
     \begin{align*}A\setminus (B\cap C)&=A\cap (B\cap C)^c \\&=A\cap (B^c\cup C^c)\\&=(A\cap B^c)\cup(A\cap C^c)\\&=~?\end{align*}
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    Re: Math Proof A-(B∩C)=(A-B)∪(A-C).

    Or use the basic definitions: if x is in A-(B\cap C) then x is in A but not in B\cap C. That, in turn, means it is either NOT in B or NOT in C.
    case 1: x is in A but not in B. Then it is in A\cap B.
    case 2: x is in A but not in C. Then it is in A\cap C.
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