Recent content by andrew1

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    MHB Proving Binary Relations: R & S

    Well when $a<b$ won't be related to a since 4 < 5 for example doesn't mean 5 < 4, but now the anti-symmetric property part of the question confuses me because if I take a as 4 again and b as 5, 4 $\ne$ 5. Would it also be sufficient to say that the relation isn't transitive as well since 1R5...
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    MHB Proving Binary Relations: R & S

    reflexivity is just aRa so I guess it would be reflexive since if I use any natural number for a it will be related to itself
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    MHB Proving Binary Relations: R & S

    Sorry about the latex commands thing, not sure how it works :S In regards to R, would a + 5 be treated as just a? therefore it isn't reflexive?
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    MHB Proving Binary Relations: R & S

    Hi, I'm currently stuck on a few questions regarding binary relations as I'm unsure on how to prove their properties. R is defined on N by aRb if and only if a <= b and b <= a+5 Is R reflexive, symmetric, antisymmetric, transitive? S is defined on Z (union) {x + 1/2 : x is an element of all...
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    MHB Breadth First and Depth First Spanning Trees

    Tried this myself the other night and got QSTUR as the last step in my breadth first spanning tree before taking out all the items from the queue, is this correct?
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    MHB Breadth First and Depth First Spanning Trees

    Hi, I'm currently stuck on how to construct a breadth first and depth first spanning tree for this graph, the algorithm that I'm following is somewhat ambiguous. I'd really appreciate if someone can provide an explanation on how I should go by doing this. Thanks
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    MHB Inhomogeneous recurrence relation

    Sorry, I meant an example of an inhomogeneous recurrence relation, I understand how to solve a homogeneous recurrence relation, but converting an inhomogeneous recurrence is where I am struggling.
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    MHB Inhomogeneous recurrence relation

    Could you possibly provide an example, this would help me understand it a bit better.
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    MHB Inhomogeneous recurrence relation

    Hi all, Could someone please explain to me the process involved in converting an inhomogeneous recurrence to a homogeneous recurrence, I'm completely confused as to how it works.Thanks
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    MHB Recursive sequences and finding their expressions

    Cheers, that's a much simpler way of thinking of solving the problem, I guess it was the fact that 2 was a double root that confused me.
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    MHB Recursive sequences and finding their expressions

    Hmmmm I tried doing this equation myself but am also stuck. I tried subbing in n=2, 3 and 4 into the equation and have found that: S2= -8 S3= -36 S4= -112 S5= -304 So the pattern that I have found is that there is a difference of -28, -76 and -192 but this doesn't lead me to an easily findable...
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    MHB How Do You Prove a Recursive Sequence Using Strong Induction?

    Hmmk, makes more sense now, strong induction always seems to confuse me :(
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    MHB How Do You Prove a Recursive Sequence Using Strong Induction?

    This part doesn't make much sense to me < $3 * 5^n + 10 * 5^{n-1}$ < $3 * 5^n + 2 * 5^n$ < $5 * 5^n $ < $5^{n+1}$
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    MHB How Do You Prove a Recursive Sequence Using Strong Induction?

    Thank you, but I'm confused as to how you arrived at that conclusion, could you provide a description of the process that you went through for each of the steps please.
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    MHB How Do You Prove a Recursive Sequence Using Strong Induction?

    Hi, I'm currently having trouble with using strong induction to prove a recursive sequence and don't know where to begin, any help would be great thanks. Define a recursive sequence f(0), f(1), f(2),... by f(0) = 0 f(1) = 1 f(n+1) = 3f(n) + 10f(n-1), for all integers n>=1 Prove by strong...