Let X, Y and Z be sets. For each of the following statements, prove it or give a counterexample.(a) If X is not a subset of Y , then Y is a subset of X.(b) (X − Y ) − X = ∅.(c) X ∪ (Y − Z) = (X ∪ Y ) − (X ∪ Z).

The statement which is true is (c) X ∪ (Y − Z) = (X ∪ Y ) − (X ∪ Z) and the

statements which are false are a) If X is not a subset of Y , then Y is a subset of X and (b) (X − Y ) − X = ∅.

The statement "If X is not a subset of Y, then Y is a subset of X" is false. A counterexample is sufficient to disprove this statement.

Let's consider X = {1, 2} and Y = {2, 3}. X is not a subset of Y because it contains the element 1 which is not in Y.

However, Y is not a subset of X either because it contains the element 3 which is not in X. Therefore, the statement is false.

The statement "(X - Y) - X = ∅" is false. To prove this, we need to find a counterexample.

Let's consider X = {1, 2, 3} and Y = {2, 3}. The set (X - Y) - X can be computed as ({1} - {2, 3}) - {1}, which simplifies to the empty set ∅. However, the statement claims that (X - Y) - X should be equal to ∅, which is false in this case. Therefore, the statement is false.

The statement "X ∪ (Y - Z) = (X ∪ Y) - (X ∪ Z)" is true. To prove this, we need to show that the sets on both sides of the equation contain the same elements.

Let's consider an arbitrary element x.

If x is in X ∪ (Y - Z), it means x is either in X or in (Y - Z). If x is in X, then it is also in X ∪ Y and X ∪ Z, so it will be in (X ∪ Y) - (X ∪ Z). If x is in (Y - Z), it is not in Z, so it will be in X ∪ Z. Therefore, x is in (X ∪ Y) - (X ∪ Z).

Conversely, if x is in (X ∪ Y) - (X ∪ Z), it means x is in X ∪ Y but not in X ∪ Z. This implies that x is either in X or in Y but not in Z. Therefore, x will be in X ∪ (Y - Z).

Since we have shown that an arbitrary element x is in both X ∪ (Y - Z) and (X ∪ Y) - (X ∪ Z), we can conclude that the two sets are equal. Hence, the statement is true.

Learn more about counterexample here:

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30 points

Syed took out a cash advance of d dollars from a financing company. The company deducts a fee of 1/3 of the orig
advanced amount along with a wire transfer fee of $30.00. What is the final advanced amount that Syed receives if she takes out a
cash advance of $300?

(Numerical Answer Only)

Can someone help me out with these?
"write a linear equation for line m,n,l,p"​

Bona ma numec claudiu si vreu sa stiu si eu cat face 100+340

I’ll give the Brainliest to who answers these questions with a reasonable explanation.

While surfing the Internet, you find a site that claims to offer “the most popular and the cheapest DVDs anywhere.” Unfortunately, the website isn’t clear about the how much they charge for each DVD, but it does give you the following information:
(The information is the table up there)

a. What is the slope of the line containing the points?

b. What does the slope represent in this problem?

c. What is the y‐intercept of the line that contains the points?

d. What does the y‐intercept represent in this context?

e. What is the equation that represents the line?

Thank you.

What is the sum of the measures of the interior angles of a 12-gon ?


A: 1620

B: 1800

C: 1980

D: 2160

plzz answer fasttttt​

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The county fair charges $.50 per ride and $10 to get
in. If you have $32, write an equation to find the
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plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helpppppppppppppp

please help solve :D

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PLEASE HELP LOOOOOOOKKKKKKKK ATT SS

Simplify the following expression 2n+6+4y-8

Solve the system of equations using the elimination method.
3x + 4y = -2
2x + 3y = -1

Please help me! 20 points!
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Multiply and simplify if possible.

√7x(√x−7√7)

Thank you lovely

Consider the line 8x+6y= 7.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?

write an expression in simplified form to represent the area of the trapezoid ​

Jon has to pay $9.00 admission for the skating rink and $2 per hour to
rent roller blades. How many hours can he skate for $19?*
3
5
06

Plz help me with this question

The bases of a trapezoid lie on the lines y=2X +7 and y= 2X -5. Write the equation that contains the midsegment of the trapezoid

The equation  is written in point-slope form. What is the equation written in slope-intercept form?    ​

I’ll mark as brainliest!!!

Find x and y plz help

Will give brainlyest (however you spell it)
Directions: Find the missing angles or arcs. Circles may not be drawn to scale.

81 - 4x = 147 please help

Whats chicken nugget plus chicken nugget​

Which conveyed the negative message?




pleasssss​

Which of the following could represent consecutive even integers?

x + 1, x + 2
x + 1, x + 3
2x, 2x + 1

Hi can anyone do this for me please do it on a piece of paper

What mathematical term describes both 5.3 and 8.2 in the expression 5.3 x − 8.2 y + 11.1 ?