 # Advanced Math Help with Any Problems!

Upper Level MathOpen question Jolina Manos2022-09-24

## How many elements are in the set {3, 3, 3, 3}

Upper Level MathOpen question orrocksydnie33 2022-09-22

## find the 52nd term of the arithmetic sequence -8,-12,-16 Sneha Loganathan2022-09-16

## Let f be the function from R to R defined by f(x)=x^2.Find f^-1({x|0<x<1})

Upper Level MathOpen question 2022-09-15

## 3y/4 - 4 = y/2 + 2 kesaiatonu2015 2022-09-13

## f(n)=  n-1

Upper Level MathOpen question rennieb2018 2022-09-11

## what is the difference between a System of equations and an Equation? Kiana Arias 2022-09-07

## Question: Provide further motivation for defining $p\to q$ to be true when p is false For the first change, we call the resulting operator imp1.Show that p imp1 q logically equivalent q imp1 p.$\begin{array}{|lll|}\hline p& q& p\phantom{\rule{thickmathspace}{0ex}}imp1\phantom{\rule{thickmathspace}{0ex}}\\ T& T& T\\ T& F& F\\ F& T& F\\ F& F& T\\ \hline\end{array}$ Frida Faulkner 2022-09-07

## Expressing statements in Discrete mathGiven thatA is the set of all Alpha'sM is the set of all Menhow do I express this statement: Not all Alpha's are Men.............My attempt:$A\subset S=0$in other words saying that A is not a subset of S, but I can't use the not subset symbol on this problem. Lucille Douglas 2022-09-07

## Question about getting a formula for a recurrence relationsSo basically, I was watching video above which is on recurrence relations and I had a question about this statement:${a}_{n}={a}_{n-1}+6{a}_{n-2}$I understand how he got the $\left(-2{\right)}^{n}$ and $\left(3{\right)}^{n}$, but not about how he is adding them and then multiplying them by the variables $\alpha$ and $\beta$. He said that there is a proof online about why there is always going to be an $\alpha$ and a $\beta$ that will always make this statement true, but I wasn't able to find it and I was hoping that somebody could give me a step by step explanation about how this is. I was also wondering about the general case for getting a formula for recurrence relations in this form.Note: I read somewhere that you can derive this from generating functions, but I don't have a strong background in them, so I was wondering if there is another way to derive the relation. Paul Reilly 2022-09-07

## Need help understanding $\mathrm{\exists }x\mathrm{\forall }yvs\mathrm{\forall }x\mathrm{\exists }y$My understanding is that for $\mathrm{\exists }x\mathrm{\forall }y$, there can only be one x value that is true for every single y value. Meaning theres only one x value (which cannot be changed) for every single different y value. The statement $\mathrm{\exists }x\mathrm{\forall }y\left(p\left(x,y\right)\right)$ is true when there is one x value (lets say $x=0$) that is true for $y=-2,-1,0,1,2$,... (for every single y). Correct me if I am wrong but this is my understanding of this notation.And now my understanding for the second notation $\mathrm{\forall }x\mathrm{\exists }y\left(p\left(x,y\right)\right)$ is that for every x value, there exists a y such that p(x,y). Meaning for every x value ($x=-2,-1,0,1,2,...$) there can be a different y value for each x value so that the statement is true.I dont really know how to explain this well but I'll try to summarize my understanding. If the notation is $\mathrm{\exists }x\mathrm{\forall }y$ then theres only one x that cannot be changed that is true for every y. If the notation is $\mathrm{\forall }x\mathrm{\exists }y$ then the y value doesnt have to be the same y value for every x value. Meaning for every x value there can be a y value that is different than another y value for another x value. Jadon Stein 2022-09-07

## Discrete Math: Combinatorics and recursion3. Let S be a set of size 37, and let x, y, and z be three distinct elements of S. How many subsets of S are there that contain x and y, but do not contain z?(a) ${2}^{33}$(b) ${2}^{34}$(c) ${2}^{35}$(d) ${2}^{37}-{2}^{35}-{2}^{36}$(d) none of the aboveWhy is it B) I thought there is size 37 so it is 37 - 2 Is it because there is size 37 and for x and y; you do 37-2. but you cannot have z so you minus another 1. so $37-2-1=34$; ${2}^{34}$12. The Fibonacci numbers are defined as follows: $f0=0,f1=1$, and $fn=fn-1+fn-2$ for $n\ge 2$. Consider again the recursive algorithm Fib, which takes as input an integer $n\ge 0$:Algorithm Fib(n):if then $f=n$else $f=Fib\left(n-1\right)+Fib\left(n-2\right)$end if;return fFor $n\ge 3$, run algorithm Fib(n) and let an be the number of times that Fib(2) is called. Which of the following is true?(a) For $n\ge 3$, ${a}_{n}={f}_{n-1}$(b) For $n\ge 3$, ${a}_{n}={f}_{n}$(c) For $n\ge 3$, ${a}_{n}={f}_{n+1}$(d) For $n\ge 3$, ${a}_{n}=-1+{f}_{n}$So if it is $n=3$ i will call fib(2) 1 time and if $n=4$ then fib(2) is called 2 timesHow do I put this into an equation like above? kybudmanqm 2022-09-07

## Let G be a 3-regular plane graph with 12 faces. How many vertices does G have?This would be pretty easy to solve if I knew that G is connected by using Eulers formula $|V|-|E|+|F|=2$.But I don't know how to show that G is connected. Am I on the wrong path? Or is there some combinatorial argument to count the vertices? calcific5z 2022-09-07

## Coefficient of expansion discrete mathWhat is the coefficient of ${x}^{12}{y}^{12}$ in the expansion of $\left(3x-7y{\right)}^{24}$? I am just checking if I answered it in the correct way. Since its the expansion to the power of 24 and $\left(xy{\right)}^{12}=\left({x}^{12}\right)\left({y}^{12}\right)$ then i Just substituted 3x and -7y with x and y. I got $\left(3x{\right)}^{12}\left(-7y{\right)}^{12}\left(\genfrac{}{}{0}{}{24}{12}\right)$. Is my reasoning correct or is there much more to this. Makayla Reilly 2022-09-07

## Let $h=g\circ f\circ g$ where $f:\mathbb{R}\to \mathbb{Z}$ is the floor function and $g:\mathbb{R}\to \mathbb{R}:x↦-x$.(i) Compute h(3.4), h(7) and h(-1.3).(ii) Describe what h is doing to a general real number x. driliwra7 2022-09-07

## I wanted to ask here if this proving process were correct:$f\left(a\right)=$ a div dWe must show this is an onto functionIf it is onto, then $\mathrm{\forall }y$ in the codomain, $\mathrm{\exists }a$ in the domain such that $f\left(a\right)=y$Consider an arbitrary y in the codomain. We know that $f\left(a\right)=y$ if and only if a div d $=y$.a div $d=y$ implies that $a=dy+r$ .But then $f\left(dy+r\right)=y$ because:$f\left(dy+r\right)$= $\left(dy+r\right)$ div d meanining that$dy+r=dq+k$ where q=$\left(dy+r\right)$ div dNow since $a=dy+r$, a mod d is equal to $\left(dy+r\right)$ mod d so $k=r$This means that:$dy+r=dq+r$, so the quotient q of $dy+r$ is y. But then $f\left(dy+r\right)=y$, so for an arbitray y, there is an element $dy+r$ in the domain such that $f\left(dy+r\right)$ is y, as we wanted to show. cjortiz141t 2022-09-07

## Relations between ordered pairs.I am completely confused about this question, everytime I look back onto it I have a different idea on how to interpret it. Any help is appreciated.A relation R is defined on ${\mathbb{Q}}^{2}$ by (a,b)R(c,d) if and only if there exists a real number $x\ge 1$ such that $a=dx$ and $c=bx$.I need to show what type of relation this is, e.g. is it reflexive, transitive, symmetric....? Right now, I am just having a lot of trouble on how to interpret this and how to actually come up with a way of proving this. calcific5z 2022-09-07

## Discrete Math (Combination with repetition)The employee is distributing 7 objects among 4 containrs (Xi's).Assuming the containers are $X1+X2+X3+X4=7$ where $Xi>=0\mathrm{\forall }1<=i<=4$.Determine all integer solutions. nar6jetaime86 2022-09-07

## Binary strings and discrete mathLet S be the set of binary strings of length 30 with 10 1’s and 20 0’s. Let A be the set of the first 30 positive integers {1,2,3,…,30}. Let B be the set of all subsets of A containing 10 numbers. Find a one-to-one correspondence between S and B. sincsenekdq 2022-09-07
## Find Upper Bound for $T\left(n\right)=T\left(n-1\right)+T\left(\frac{n}{2}\right)+n$ with recursive tree method. Kaleigh Ayers 2022-09-07