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Math Help - Proof of the subset equality (using Boolean algebra logic)

  1. #1
    Member Pranas's Avatar
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    Proof of the subset equality (using Boolean algebra logic)

    Using Boolean algebra logic I am asked to prove

    \displaystyle \[A \subseteq B \Rightarrow \overline B  \subseteq \overline A \]

    In mathematical analysis course that looks like plain and simple modus tollens principle, but using Boolean algebra logic I just don't know...

    Maybe you can help me?
    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Pranas View Post
    Using Boolean algebra logic I am asked to prove \displaystyle \[A \subseteq B \Rightarrow \overline B  \subseteq \overline A \]
    In mathematical analysis course that looks like plain and simple modus tollens principle, but using Boolean algebra logic I just don't know...
    That is just the contra-positive of a statement.
    "If P then Q" is true then "If not Q then not P" is also true.
    If x\in A then x\in B is equivalent to If x\notin B then x\notin A.
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