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Math Help - Answer is OR, why not UNION?

  1. #1
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    Answer is OR, why not UNION?

    Still working on a test review here, havent seen this one in my home work.

    x-9
    --- > 0
    x+7

    x=9 and x=-7

    Test it on the number line, end up with

    (-(infinity symbol),-7) as well as (9,(infinity symbol))

    Normall, I type the UNION symbol in these problems, but the answer is showing OR, so the answer shows:


    (-(infinity symbol),-7) OR (9,(infinity symbol))


    I don't understand this curve ball.
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  2. #2
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    Re: Answer is OR, why not UNION?

    Quote Originally Posted by itgl72 View Post
    Still working on a test review here, havent seen this one in my home work.
    x-9
    --- > 0
    x+7
    x=9 and x=-7
    Test it on the number line, end up with
    (-(infinity symbol),-7) as well as (9,(infinity symbol))
    Normall, I type the UNION symbol in these problems, but the answer is showing OR, so the answer shows:
    (-(infinity symbol),-7) OR (9,(infinity symbol))
    I don't understand this curve ball.
    Union means or.
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  3. #3
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    Re: Answer is OR, why not UNION?

    Quote Originally Posted by Plato View Post
    Union means or.

    Can it really be that easy? :-) Been stressing here since I saw it. Why does that teacher throw me curveballs when Im on the edge already? LOL!!
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  4. #4
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    Re: Answer is OR, why not UNION?

    Quote Originally Posted by itgl72 View Post
    Why does that teacher throw me curveballs when Im on the edge already? LOL!!
    because she/he can ...
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  5. #5
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    Re: Answer is OR, why not UNION?

    Strictly speaking, the union symbol ∪ connects sets while OR connects propositions, i.e., something that can be true or false. Thus, we can write (-infinity, -7) ∪ (9, infinity). We can also write (x < -7) OR (x > 9). It is not correct to write (-infinity, -7) OR (9, infinity) and neither is (x < -7) ∪ (x > 9).

    As Plato said, there is a close connection between ∪ and OR. Let P(x) and Q(x) be some propositions containing x, e.g., P(x) is x < -7 and Q(x) is x > 9. Let A be the set of all x that satisfy P(x) and let B be the set of all x that satisfy Q(x). In this example, A = (-infinity, -7) and B = (9, infinity). Then A ∪ B is the set of all x that satisfy (P(x) OR Q(x)).

    This is probably beyond the scope of your course, so it's not terribly important for now.
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