Week 1: Assignment

First Assignment

Instructions

Solve these problems, type your solution in a word-processor such as MS Word, Google Doc, or Overleaf, and submit the PDF of your solutions. Note that only PDF files are accepted for submission. You are strongly encouraged to type the equations and formulas with an equation editor.

On the top of the first page, please type the following pledge:

"I have not received unauthorized aid on this assignment. I understand the answers that I have submitted. The answers submitted have not been directly copied from another source, but instead are written in my own words."

Assignment Details

1) Write down all the subsets of the following set:

A={1,a,{2,b}}

(5 points)

2) For the following sets

A = {a,b,c}

and

B = {a,d,e}

find the followings:

a) $A\cap B$

b) $A-B$

c) $B-A$

d) $\left(A-B\right)\cup\left(B-A\right)$

(20 points)

3) Determine the following summation in closed-form

$S=\sum_{i=0}^{n-1}\left(\frac{1}{2}\right)^i+2i$

(10 points)

4) Find the inverse of the following function:

$f\left(x\right)=x^2-1$

when the domain and target of the function is the set of non-negative integers.

(5 points)

5) Find the value of $x,y,z$ in the following vector equation:

$\begin{bmatrix} 4 \\ -2\\ 2 \end{bmatrix}+2\begin{bmatrix} x \\ 1\\ y \end{bmatrix}-3\begin{bmatrix} 2x \\ 3\\ -1 \end{bmatrix}=\begin{bmatrix} 6 \\ z\\ 2 \end{bmatrix}$

(10 points)