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Thread: Discrete Maths Sem 2 2016

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    Ancient Orator leehuan's Avatar
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    Discrete Maths Sem 2 2016

    Don't mind me...just setting up some threads for more of my stupidity this upcoming semester.

    UNSW course outline: https://www.maths.unsw.edu.au/sites/...81-s2_2016.pdf

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    Ancient Orator leehuan's Avatar
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    Re: Discrete Maths Sem 2 2016






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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post




    A is an element of B, but not a subset (assuming the b's aren't coincidentally just equal to the a's).

    Since A isn't a subset of B, it's not in the power set of B. But {A} is in P(B), since {A} is a subset of B, since A is an element of B.

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    Ancient Orator leehuan's Avatar
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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by InteGrand View Post
    A is an element of B, but not a subset (assuming the b's aren't coincidentally just equal to the a's).

    Since A isn't a subset of B, it's not in the power set of B. But {A} is in P(B), since {A} is a subset of B, since A is an element of B.
    Alright this last bit was what I needed to see. I need to have my foundations but just making sure:


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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post
    Alright this last bit was what I needed to see. I need to have my foundations but just making sure:

    That's correct (by definition of subset essentially) .
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    Re: Discrete Maths Sem 2 2016

    ahahahaha goodluck with that subject



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    Re: Discrete Maths Sem 2 2016

    Can I please have my proof checked?



    The video solution was clever in how it used a Pythagorean identity here to match up A and B, however I did it by solving. Just want to check on its validity




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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post
    Can I please have my proof checked?



    The video solution was clever in how it used a Pythagorean identity here to match up A and B, however I did it by solving. Just want to check on its validity



    A is a proper subset of B, since there are elements in B that are not in A. You are claiming that A is the set B itself.

    Recall that sinx = 0 does not imply cosx = 1

    The solutions to sinx = 0 can be divided into the solutions to cosx = 1 and cosx = -1

    Edit: sorry did not read the final line

    Yes it looks good.
    Last edited by Paradoxica; 26 Jul 2016 at 10:37 AM.
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    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by Paradoxica View Post
    A is a proper subset of B, since there are elements in B that are not in A. You are claiming that A is the set B itself.

    Recall that sinx = 0 does not imply cosx = 1

    The solutions to sinx = 0 can be divided into the solutions to cosx = 1 and cosx = -1

    Edit: sorry did not read the final line


    Yes it looks good.
    Lol. Yeah the question first asked to prove it was just a subset before claiming it was a proper subset. So I put x=π on the end to contradict they're the same set.

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    Re: Discrete Maths Sem 2 2016

    Should be ez
    "I have crippling depression" -Mahatma Gandhi
    Quote Originally Posted by Katsumi View Post
    lol

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    Re: Discrete Maths Sem 2 2016



    They don't have an answer so I am suspecting that my answer is wrong lol. I started from the outside in my working.



    Edit: After line 2 one of my friends used associativity like this



    But ends up with a final answer of just instead. Is this justified?
    Last edited by leehuan; 27 Jul 2016 at 3:37 PM.

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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post
    Can I please have my proof checked?



    The video solution was clever in how it used a Pythagorean identity here to match up A and B, however I did it by solving. Just want to check on its validity



    just fyi on the second line of the A it reads "Let A be the set of x in the real numbers such that k is in the integers such that x = 2k*pi" which makes zero sense

    try

    B Arts / B Science (Advanced Mathematics), UNSW

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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by Shadowdude View Post
    just fyi on the second line of the A it reads "Let A be the set of x in the real numbers such that k is in the integers such that x = 2k*pi" which makes zero sense

    try

    That was a part of why I put that question up. What's the difference between using | and ,

    Edit, ok my prediction is | means such that whereas , means where. In that case, if the second | was replaced with , would that still be nonsensical?
    Last edited by leehuan; 27 Jul 2016 at 3:38 PM.

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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post


    They don't have an answer so I am suspecting that my answer is wrong lol. I started from the outside in my working.



    Edit: After line 2 one of my friends used associativity like this



    But ends up with a final answer of just instead. Is this justified?
    To get the final answer your friend got (which looks correct), use an absorption law at the second last line of your proof. (Unfortunately your simplification in your last line isn't valid. But if we just apply the absorption law there we'll get the answer. )

    (See: https://proofwiki.org/wiki/Absorptio...h_Intersection.)
    Last edited by InteGrand; 27 Jul 2016 at 3:43 PM.
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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by InteGrand View Post
    To get the final answer your friend got (which looks correct), use an absorption law at the second last line of your proof. (Unfortunately your simplification in your last line isn't valid. But if we just apply the absorption law there we'll get the answer. )

    (See: https://proofwiki.org/wiki/Absorptio...h_Intersection.)
    Ahh I absorbed wrong

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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post


    They don't have an answer so I am suspecting that my answer is wrong lol. I started from the outside in my working.



    Edit: After line 2 one of my friends used associativity like this



    But ends up with a final answer of just instead. Is this justified?
    Yes what your friend did is valid. Since intersection is both associative and commutative, we can do intersections in any order (like, (X cap Y) cap Z = X cap (Y cap Z) = X cap (Z cap Y) = (X cap Z) cap Y, using associativity and commutativity. I used 'cap' to mean intersection symbol.). Then using absorption law finishes it.
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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post
    That was a part of why I put that question up. What's the difference between using | and ,

    Edit, ok my prediction is | means such that whereas , means where. In that case, if the second | was replaced with , would that still be nonsensical?
    Don't view "," and "|" in the same way (btw ":" is a common alternative for "|" that is my personal preference). The former is basically informal formatting here, whilst the latter is part of the formal set builder notation syntax.

    {x in A: Mathematical statement P(x) about x}

    is the general way of denoting the collection of x in A such that P(x) is true. Comma is just formatting of that mathematical statement in this case, to be translated as "for some". Although this certainly isn't unambiguous notation, its intended meaning should be pretty obvious from context. We are often slightly lazy in writing mathematical statements because writing things formally with quantifiers in each line would be needlessly tedious in long proofs.
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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post
    That was a part of why I put that question up. What's the difference between using | and ,

    Edit, ok my prediction is | means such that whereas , means where. In that case, if the second | was replaced with , would that still be nonsensical?
    no, but then you're saying the set consists of x and k, when you really want to just have the x's that satisfy the condition


    the thing i wrote reads "x in the real numbers such that x = 2k*pi where k is any integer"
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    B Arts / B Science (Advanced Mathematics), UNSW

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    Re: Discrete Maths Sem 2 2016

    This bugger.


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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post
    This bugger.

    if i remember its easier to prove by Venn Diagrams



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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post
    This bugger.





    Last edited by InteGrand; 27 Jul 2016 at 10:14 PM.
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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by RenegadeMx View Post
    if i remember its easier to prove by Venn Diagrams
    Sounds right. Jim Franklin seems to prefer to drill us into using slightly more formalised proofs though.

    I just wasn't sure how to manipulate my x in. And yet again I forgot that you had to prove they are a mutual subset of each other to be equal sets.

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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post
    Sounds right. Jim Franklin seems to prefer to drill us into using slightly more formalised proofs though.

    I just wasn't sure how to manipulate my x in. And yet again I forgot that you had to prove they are a mutual subset of each other to be equal sets.
    havent heard of him before, but had a look at your course outline you lucky fucks will have peter brown
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    Quote Originally Posted by Shadowdude View Post
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    Quote Originally Posted by Shadowdude View Post
    who cares about your timetable - you should be going into uni every day to study and do whatever regardless

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    Re: Discrete Maths Sem 2 2016



    I can see why it is but how would you prove it

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    Re: Discrete Maths Sem 2 2016

    Quote Originally Posted by leehuan View Post


    I can see why it is but how would you prove it


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