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    hi guys, how do u prove this

    1) "If A U (B-A) is not a subset of B, then A cannot be a subset of B" .
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    All the elements of (B-A) are in B, so if A U (B-A) isn't a subset of B, then at least one of the elements of A isn't in B.
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    (Original post by yagmai)
    hi guys, how do u prove this

    1) "If A U (B-A) is not a subset of B, then A cannot be a subset of B" .
    There exists some x \in A \cup (B-A) such x \not\in B as  A \cup (B-A) is not a subset of B
    x \in A or x \in (B-A) but x \not\in B so x \not\in (B-A) and so x \in A
    Thus x \in A but x \not\in B and thus as a typical element of A is not in B we have proved A is not a subset of B.
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    (Original post by Gaz031)
    There exists some x \in A \cup (B-A) such x \not\in B as  A \cup (B-A) is not a subset of B
    x \in A or x \in (B-A) but x \not\in B so x \not\in (B-A) and so x \in A
    Thus x \in A but x \not\in B and thus as a typical element of A is not in B we have proved A is not a subset of B.
    Yep, pretty standard proof. Gaz031, is that LaTeX you're using? I've been trying to look for it, do you have any idea where I can download it?
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    (Original post by HTale)
    Yep, pretty standard proof. Gaz031, is that LaTeX you're using? I've been trying to look for it, do you have any idea where I can download it?
    Yes it's TeX though i'm using the forum plugin - I didn't need to use any software from my computer.

    To use it on the forum you simply write the TeX content between [ tex] and [ /tex] tags (delete the space) - you can click on reply to see the actual input.

    If you want to use the proper software on your computer that has many many more features for producing proper documents then it might be a good idea to follow the instructions to install software here:
    http://www.artofproblemsolving.com/L...PS_L_About.php

    For more in depth tutorials try:
    http://www.ctan.org/tex-archive/info/gentle/
    http://www.maths.tcd.ie/%7Edwilkins/LaTeXPrimer/
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    (Original post by Gaz031)
    There exists some x \in A \cup (B-A) such x \not\in B as  A \cup (B-A) is not a subset of B
    x \in A or x \in (B-A) but x \not\in B so x \not\in (B-A) and so x \in A
    Thus x \in A but x \not\in B and thus as a typical element of A is not in B we have proved A is not a subset of B.
    a subset of B.
    wow..thanks alot for ur help.

    I have another qns. How do i approach this qns?

    Let R1 and R2 be relations on a set A, Prove or
    a) R1 and R2 reflexive => R1 n R2 reflexive
    c) R1 and R2 antisymmetrix => R1 n R2 antisymmetrix
    d) R1 and R2 transitive => R1 n R2 transitive
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    (Original post by Gaz031)
    There exists some x \in A \cup (B-A) such x \not\in B as  A \cup (B-A) is not a subset of B
    x \in A or x \in (B-A) but x \not\in B so x \not\in (B-A) and so x \in A
    Thus x \in A but x \not\in B and thus as a typical element of A is not in B we have proved A is not a subset of B.
    :eek:

    Ahh I should have looked over some of this, really.
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    I have another qns. How do i approach this qns?
    Sorry - I can't help you with those as I haven't covered that material. I'm sure someone else can help though

    Ahh I should have looked over some of this, really.
    I don't know much about them really - I was just fortunate I knew enough to have a go at the first one! In fact I looked up B-A just to check it meant what my intuition told me it did!
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    (Original post by yagmai)
    Let R1 and R2 be relations on a set A, Prove or
    a) R1 and R2 reflexive => R1 n R2 reflexive
    c) R1 and R2 antisymmetrix => R1 n R2 antisymmetrix
    d) R1 and R2 transitive => R1 n R2 transitive
    (a,a) is in R1 and R2 for all a so (a,a) is in R1 n R2 for all a

    This proves (a).

    If (a,b) and (b,a) lie in R1nR2 then they both lie in R1 and R2

    As R1 is antisymmetric then a=b (you only need one of R1,R2 to be AS).

    Hence R1nR2 is antisymmetric.

    This proves (c).

    I imagine you can do (d) with this help.
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    (Original post by Gaz031)
    Yes it's TeX though i'm using the forum plugin - I didn't need to use any software from my computer.

    To use it on the forum you simply write the TeX content between [ tex] and [ /tex] tags (delete the space) - you can click on reply to see the actual input.

    If you want to use the proper software on your computer that has many many more features for producing proper documents then it might be a good idea to follow the instructions to install software here:
    http://www.artofproblemsolving.com/L...PS_L_About.php

    For more in depth tutorials try:
    http://www.ctan.org/tex-archive/info/gentle/
    http://www.maths.tcd.ie/%7Edwilkins/LaTeXPrimer/
    :top: Thanks alot mate.
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