Recent content by andrew1

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...

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

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?

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...

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?

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

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.

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

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

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.

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...

Hmmk, makes more sense now, strong induction always seems to confuse me :(

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 $ < $5^{n+1}$

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.

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...