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Thread: Truth table correct?

  1. #1
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    Truth table correct?

    Is this truth table correct?

    Thanks

    Edit: should be $\displaystyle x \in A $, $\displaystyle x \in B $ etc...

    For the last two I thought of them like this: If $\displaystyle x \in A, x \in B $ then $\displaystyle x \in A \cup B $ is true. However if $\displaystyle x \in C $ then $\displaystyle x \in (A \cup B) - C $ is false. So we require that $\displaystyle x \not \in C $ for the statement to be true. So the $\displaystyle '-' $ operation is sort of like the $\displaystyle \cap $ operation in terms of truths.

    Crap...just realized I screwed up. For all $\displaystyle x \in C $ then the second to last statement is false. For all $\displaystyle x \not \in C $ then that statement is true.

    The last one is basically a union of two sets. So to be false, $\displaystyle x \not \in A-B $ and $\displaystyle x \not \in C $
    Attached Thumbnails Attached Thumbnails Truth table correct?-untitled.jpg  
    Last edited by shilz222; Aug 8th 2007 at 01:22 PM.
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  2. #2
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    Frankly, I am not at all sure what you are trying to do here.
    Not sure how your text/instructor applies truth-values to sets.

    However, here is the traditional understanding.
    $\displaystyle \left( {A \cup B} \right) - C$ would be (A or B) and not C; $\displaystyle \left( {A \vee B} \right) \wedge (\neg C)$.

    Whereas $\displaystyle \left( {A - B} \right) \cup C$ would be (A and not B) or C; $\displaystyle \left( {A \wedge \neg B} \right) \vee C$.

    This is not what your table of values represents!
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  3. #3
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    Thats why I added the $\displaystyle x \in A, x \in B \ldots $.

    Otherwise they wouldn't be statements (i.e. you can't say the set $\displaystyle A $ is false).
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  4. #4
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    Quote Originally Posted by shilz222 View Post
    Thats why I added the $\displaystyle x \in A, x \in B \ldots $. Otherwise they wouldn't be statements (i.e. you can't say the set $\displaystyle A $ is false).
    But even with those additions, what in what sense does it make to assign a truth-value to $\displaystyle x \in A$?

    Are you try to decide the truth-value of:
    $\displaystyle \text{If}\;x \in A,\;x \in B\;\text{and}\;x \notin C\;\text{then}\;x \in \left( {A \cup B} \right) - C$?
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  5. #5
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    No I am trying to do the following:

    $\displaystyle x \in A, \ x \in B, \ x \in C, \ x \in (A \cup B) - C, \ x \in (A-B) \cup C $ are all statements.

    Therefore we can assign truth values to them. So for the statement $\displaystyle x \in (A \cup B) - C $ to be true, we require that $\displaystyle x \not \in C $ or $\displaystyle x \in C $ to be false right? If $\displaystyle x \in C $ then the statement $\displaystyle x \in (A \cup B) - C $ is false (looking at a venn-diagram).

    So the statement $\displaystyle x \in A $ is true means $\displaystyle x \in A $.

    If the statement $\displaystyle x \in A $ is false then $\displaystyle x \not \in A $.
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  6. #6
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    Well I would expect that it means this:
    Attached Thumbnails Attached Thumbnails Truth table correct?-tr_tbl.gif  
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  7. #7
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    Yes that what I meant in my first post (with the $\displaystyle x \in A $ $\displaystyle x \in B $ etc..).

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