# Let A_{2}A_{2} be the set of all multiples of 2 except for 2.2. Let A_{3}A_{3} be the set of all multiples of 3 except for 3. And so on, so that A_{n}A_{n} is the set of all multiples of nn except for n,n, for any ngeq2.ngeq2. Describe (in words) the set A_{2} cup A_{3} cup A_{4} cup... Question
Discrete math Let $$\displaystyle{A}_{{{2}}}{A}_{{{2}}}$$ be the set of all multiples of 2 except for 2.2. Let $$\displaystyle{A}_{{{3}}}{A}_{{{3}}}$$ be the set of all multiples of 3 except for 3. And so on, so that $$\displaystyle{A}_{{{n}}}{A}_{{{n}}}$$ is the set of all multiples of nn except for n,n, for any $$\displaystyle{n}\geq{2}.{n}\geq{2}$$. Describe (in words) the set $$\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots$$ 2021-01-06
Step 1
Let A and B be two sets. Then the union of two sets will be the set that will contain all the elements that are either in set A, either in set B or in both A and B.
Step 2
As set $$\displaystyle{A}_{{{2}}}{A}_{{{2}}}$$ contains all ordered pairs that are multiple of 2 except 2. In the same manner for the other pairs.
Thus, set $$\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup{A}_{{{5}}}\ldots\ldots.$$ will contain all natural numbers except the prime numbers and 1.

### Relevant Questions Im confused on this question for Discrete Mathematics.
Let $$\displaystyle{A}_{{{2}}}$$ be the set of all multiples of 2 except for 2. Let $$\displaystyle{A}_{{{3}}}$$ be the set of all multiples of 3 except for 3. And so on, so that $$\displaystyle{A}_{{{n}}}$$ is the set of all multiples of n except for n, for any $$\displaystyle{n}\geq{2}$$. Describe (in words) the set $$\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots$$. The following problem is solved by using factors and multiples and features the strategies of guessing and checking and making an organized list.
Problem
A factory uses machines to sort cards into piles. On one occasion a machine operator obtained the following curious result.
When a box of cards was sorted into 7 equal groups, there were 6 cards left over, when the box of cards was sorted into 5 equal groups, there were 4 left over, and when it was sorted into 3 equal groups, there were 2 left.
If the machine cannot sort more than 200 cards at a time, how many cards were in the box? Let the universal set the set of R of all real numbers and
Let $$A={x in R|-1 a:find \(A cup B$$
b:Find $$A cap B$$
c:Find $$A^c$$ For each positive integer n, find the number of positive integers that are less than 210n which are odd multiples of three that are not multiples of five and are not multiples of seven. Justify your answer, which should be in terms of n. For the following, write your list in increasing order, separated by commas.
a, List the first 10 multiples of 8.
b. LIst the first 10 multiples on 12.
c. Of the lists you produced in parts a. and b., list the multiples that 8 and 12 have in common.
d. From part c., what is the smallest multiple that 8 and 12 have in common. Using cardinatility of sets in discrete mathematics the value of N is real numbers Currently using elements of discrete mathematics by Richard Hammack chapter 18 Let A be a collection of sets such that X in A if and only if $$X \supset N\ \text{and} |X| = n$$ for some n in N. Prove that $$|A| = |N|$$.   Let $$\displaystyle{F}_{{i}}$$ be in the $$\displaystyle{i}^{{{t}{h}}}$$ Fibonacc number, and let n be ary positive eteger $$\displaystyle\ge{3}$$
$$\displaystyle{F}_{{n}}=\frac{1}{{4}}{\left({F}_{{{n}-{2}}}+{F}_{{n}}+{F}_{{{n}+{2}}}\right)}$$ 1. Find each of the requested values for a population with a mean of $$? = 40$$, and a standard deviation of $$? = 8$$ A. What is the z-score corresponding to $$X = 52?$$ B. What is the X value corresponding to $$z = - 0.50?$$ C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of $$M=42$$ for a sample of $$n = 4$$ scores? E. What is the z-scores corresponding to a sample mean of $$M= 42$$ for a sample of $$n = 6$$ scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: $$a. -2.00 b. 1.25 c. 3.50 d. -0.34$$ 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $$\mu = 78$$ and $$\sigma = 12$$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $$82, 74, 62, 68, 79, 94, 90, 81, 80$$. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $$12 (\mu = 42, \sigma = 12)$$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is$44.50 from tips. Test for a difference between this value and the population mean at the $$\alpha = 0.05$$ level of significance.