All categories

3 years ago

In proper paragraph form,explain the difference between the union and intersection of two sets.

Mathematics

2 answers:

Sophie [7]3 years ago

6 0

The <em><u>correct answer</u></em> is:

The union of two sets is a combination of all elements from both sets. The intersection of two sets, on the other hand, is a set of the elements common to both sets.

For instance, if we have the sets {1, 3, 5, 7, 9} and {3, 6, 9, 12, 15}, the union would be the combination of both:

{1, 3, 5, 6, 7, 9, 12, 15}

The intersection of the sets would be the common elements. The only elements that are in both sets are 3 and 9. This makes the intersection

{3, 9}

siniylev [52]3 years ago

4 0

Answer: The union of two sets, A and B, is a set whose elements are those that appear in either Set A or Set B without repetition. Without repetition means that elements in both A and B need to be listed only once in the union. The union combines every element from Set A and Set B. The symbol for union is. The intersection of two sets, A and B, is a set whose elements are those that are common to A and B. This means the set includes only the elements that are found in both Set A and Set B. The symbol for intersection is.

Example of Union: If A = {. . ., -3, -2, -1} and B = {0, 1, 2, 3, . . .}, then A B = {. . ., -3, -2, -1, 0, 1, 2, 3, . . .}, or the Integers.

Example of intersection: If A = {1, 2, 3} and B = {2, 3, 4}, then A B = {2, 3}, the elements in both set A and set B.

You might be interested in

Select the correct answer. Sean and Colleen are raking leaves in their yard. Working together, they can clear the yard of leaves

Lera25 [3.4K]

Answer:

40 minutes

Step-by-step explanation:

Let c represent the number of minutes it would take colleen to finish the job when he is working alone. Hence, it can be represented by the equation:

$\frac{1}{c}+\frac{1}{c+20} =\frac{1}{24} \\\\Finding\ the\ L.C.M\ of\ the\ fraction\ to\ get\ 24c(c+20)\ as\ the\ L.C.M.\\Multiply\ the\ whole\ equation\ by\ 24c(c+20):\\\\\frac{1}{c}(24c(c+20))+\frac{1}{c+20}(24c(c+20)) =\frac{1}{24}(24c(c+20)) \\\\24c+480+24c=c^2+20c\\\\48c+480=c^2+20c\\\\c^2+20c-48c-480=0\\\\c^2-28c-480=0$

Solving the quadratic equation to get c gives:

c = -12 and c = 40

Since the time cannot be negative, hence c = 40 minutes.

It would take colleen 40 minutes to clear the yard of leaves alone

6 0

3 years ago

On Sunday, a local hamburger shop sold a combined total of 428 hamburgers and cheeseburgers. The number of cheese burgers sold w

melisa1 [442]

The equation you can use is x + 3x = 428 with x as the number of cheeseburgers and 3x the number of hamburgers
you solve for x and get 4x= 428 and x=107

so 321 hamburgers were sold that day.

5 0

3 years ago

A genetic experiment involving peas yielded one sample of offspring consisting of 420 green peas and 174 yellow peas. Use a 0.01

slavikrds [6]

Answer:

a) $z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

b) For this case we need to find a critical value that accumulates $\alpha/2$ of the area on each tail, we know that $\alpha=0.01$ , so then $\alpha/2 =0.005$ , using the normal standard table or excel we see that:

$z_{crit}= \pm 2.58$

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.

Step-by-step explanation:

Data given and notation

n=420+174=594 represent the random sample taken

X=174 represent the number of yellow peas

$\hat p=\frac{174}{594}=0.293$ estimated proportion of yellow peas

$p_o=0.23$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of yellow peas is 0.23:

Null hypothesis: $p=0.23$

Alternative hypothesis: $p \neq 0.23$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>3.649)=0.00026$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) Critical value

For this case we need to find a critical value that accumulates $\alpha/2$ of the area on each tail, we know that $\alpha=0.01$ , so then $\alpha/2 =0.005$ , using the normal standard table or excel we see that:

$z_{crit}= \pm 2.58$

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.

5 0

3 years ago

In the sixth grade, each student will get 4 new books. There is one class of 15 students and one class of 20 students. The expre

kipiarov [429]

I don't think this is correct but. 60+80=140 or 4(35)

5 0

3 years ago

Read 2 more answers

.................................................................. help ,,,,,

alexandr402 [8]

Answer:

Possible answer: 5a/ -6

Step-by-step explanation:

Not 100% sure to be honest.

3 0

3 years ago