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Math Help - find following sets help

  1. #1
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    find following sets help

    Hey guys, need help with this one.

    Let \varepsilon = \mathbb{R}, A = \{ x \epsilon \mathbb{R} : x > 0 \} , B = \{ x \epsilon \mathbb{R} : x > e \} , C = \{ x \epsilon \mathbb{R} : x < \pi \} , where e = 2.718 and  \pi = 3.142. Find the following sets:

    a)
    A \cup B

    My Answer: x > 0

    b) B \cup C

    My Answer: e < x < \pi

    c) A \cap B

    My Answer: x > e

    d) B \cap C

    My Answer:
     e < x < \pi

    e) \overline{A}

    My Answer: x \leq 0

    f) \overline{C}

    My Answer: x \geq \pi

    g)
    A \backslash B

    My Answer: Not sure!

    h) B \backslash C

    My Answer: Not sure!

    Any help and check on my answers would be much appreciated!
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  2. #2
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    Hello!

    I am afraid somethings wrong there

    Quote Originally Posted by jvignacio View Post
    Hey guys, need help with this one.

    Let \varepsilon = \mathbb{R}, A = \{ x \epsilon \mathbb{R} : x > 0 \} , B = \{ x \epsilon \mathbb{R} : x > e \} , C = \{ x \epsilon \mathbb{R} : x < \pi \} , where e = 2.718 and  \pi = 3.142. Find the following sets:

    a)
    A \cup B

    My Answer: x > 0
    Yes!

    Quote Originally Posted by jvignacio View Post

    b) B \cup C

    My Answer: e < x < \pi
    No!
    You should get suspiscious because of d).

    It is ,

    What does that mean? Well, it's like the intervall  (-\infty, \pi)

    x should be smaller than pi. Minus 50013 is smaller than pi, isn't it?

    ,

    is similar to x\in (e, + \infty)

    e < pi, so B u C = IR


    Quote Originally Posted by jvignacio View Post
    c) A \cap B

    My Answer: x > e

    d) B \cap C

    My Answer:
     e < x < \pi

    e) \overline{A}

    My Answer: x \leq 0

    f) \overline{C}

    My Answer: x \geq \pi
    Yep, that's correct.

    Quote Originally Posted by jvignacio View Post

    g)
    A \backslash B

    My Answer: Not sure!
    A = (0, \infty)

    because A is defined for all x > 0

    The set B is defined for all x > e

    so B = (e, \infty)

    A without B = (0, e), e. g.

    Edit: Ops, that would be B = \{ x \in \mathbb{R} : 0 < x < e \} I'm sorry, I used the wrong definition of B

    A \backslash B = \{ x \in \mathbb{R} : 0 < x < e  \}

    Quote Originally Posted by jvignacio View Post

    h) B \backslash C

    My Answer: Not sure!
    B = (0, e)

    C = (-\infty, pi)

    Note that pi > e, so B \subset C

    That's why B \backslash C = \emptyset
    Last edited by Rapha; April 16th 2010 at 09:26 PM. Reason: mostly LaTeX
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  3. #3
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    Quote Originally Posted by Rapha View Post
    Hello!

    I am afraid somethings wrong there




    No!
    You should get suspiscious because of d).

    It is ,

    What does that mean? Well, it's like the intervall ( -\infty, \pi)

    x should be smaller than pi. Minus 50013 is smaller than pi, isn't it?

    ,

    is similar to (e, + \infty)

    e < pi, so B u C = IR
    thanks for the reply! does IR mean all Real numbers?
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  4. #4
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    Quote Originally Posted by jvignacio View Post
    thanks for the reply! does IR mean all Real numbers?
    You're welcome.

    IR is supposed to mean the real numbers. I was kinda lazy using LaTeX, sorry for that

    (-\infty, 3.14) \cup (2.718, + \infty) = (-\infty, +\infty) = \mathbb{R}
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  5. #5
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    Quote Originally Posted by Rapha View Post
    You're welcome.

    IR is supposed to mean the real numbers. I was kinda lazy using LaTeX, sorry for that

    (-\infty, 3.14) \cup (2.718, + \infty) = (-\infty, +\infty) = \mathbb{R}
    ahh yeah thanks for that! Also is A \backslash B the same as  A - B ? meaning A without B....
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  6. #6
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    Quote Originally Posted by Rapha View Post

    h) B \backslash C

    My Answer: Not sure!


    B = (0, e)

    C = ( -\infty, \pi)

    Note that pi > e, so B \subset C

    That's why B \backslash C = \emptyset
    Sorry isn't B = (e, \infty) ? not B = (0, e)

    So B without C = x > \pi ?
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  7. #7
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    Quote Originally Posted by jvignacio View Post
    Sorry isn't B = (e, \infty) ? not B = (0, e)

    So B without C = x > \pi ?

    Arghhhh ****

    You're right! B = (0, \infty). So B without C = x > \pi is correct


    ahh yeah thanks for that! Also is the same as ? meaning A without B....
    Probably not, what is the definition of A-B?
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  8. #8
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    Quote Originally Posted by Rapha View Post
    Arghhhh ****

    You're right! B = (0, \infty). So B without C = x > \pi is correct




    Probably not, what is the definition of A-B?


    Ummm i thought it ment the same thing! If it doesn't Im not sure what the meaning of it is
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  9. #9
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    Quote Originally Posted by jvignacio View Post


    Ummm i thought it ment the same thing! If it doesn't Im not sure what the meaning of it is
    ...Could be.

    It depends on the definition you use.

    If A\backslash B = \{ x \in A : x \notin B \} := A - B then they are the same, but I know the definition

    A - B = \{ x - y : x \in A, y \in B \}

    as well. That would be something different.
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  10. #10
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    Quote Originally Posted by Rapha View Post
    ...Could be.

    It depends on the definition you use.

    If A\backslash B = \{ x \in A : x \notin B \} := A - B then they are the same, but I know the definition

    A - B = \{ x - y : x \in A, y \in B \}

    as well. That would be something different.
    Ill get back to you thanks for the help mate!
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