Description

I will give your more informations after you received this order

2 attachmentsSlide 1 of 2attachment_1attachment_1attachment_2attachment_2

Unformatted Attachment Preview

1. For the holidays, you are planning to have either a Christmas tree or

no tree in the corner of the living room. If and only if you have a

tree, you have exactly one of 4 different choices of the tree (fir, pine,

banana, and spruce) and exactly one of 3 different types of ornaments

(stars, bananas, or balls). If you do not have a tree, you can get up to

5 boxes (including 0) of presents in the corner of the room. We only

care about the set of objects in the corner of the room, and all other

information not mentioned here (type of present, size of boxes, physical

location, etc.) is considered irrelevant for this problem. How many

different possible configurations are there for decorating the corner of

the room? (as an example, one possible configuration is “a pine tree

with ball decorations” and another is “no tree and 4 boxes”)

2. Suppose V6 is rational (optional: you can prove this look it up if

you want; it is educational but hard if you haven’t seen it). Prove

or disprove: V2 + V3 is rational, (hint: you probably want to prove

something like: “if x is rational and y is rational, ay is rational.”)

3. For this problem, we define sets X = {Alice, Bob, Carol} and Y

{Red, White, Blue},

(a) How many bijective functions are there from X to Y?

(b) How many relations that are not functions are there from X to

Y?

(c) Is it possible that there exists an injective function f : X+Y

where the range of f is not equal to its codomain? Why or why

not?

(d) What about a surjective function?

4. Can you make change for 137 dollars with only 3 dollar and 12 dollar

bills in the world? Prove if you can or cannot

5. The law says “if you are not over 21 then you cannot drink.” You work

for a bar and your goal is to prevent people from breaking the law.

1

You can either check (a) people who are drinking or (b) people who

are not drinking, and then punish them (c) if they are over 21 or (d) if

they are under 21. Which of (a) or (b) are you picking? Which of (c)

or (d) are you picking? Why? (your solution must involve statement

forms and logic, not just “English” deduction)

6. You need to pick a captain and 2 sub-captains (all 3 people must be

different to make a team of 3 from a set of n people. (For example,

if the n = 5 people are Alice, Bob, Carol, DeAngelo, and Egani, one

choice of the team is Carol is the captain and Alice and De Angelo are

co-captains. The order of the co-captains do not matter). How many

ways to do this are there?

Purchase answer to see full

attachment

Tags:

rational number

Injective function

algebraic operations

possible conjugations

number of functions

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

## Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.