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.

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

Plz help me with this question

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
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(Numerical Answer Only)

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

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B: 1800

C: 1980

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3
5
06

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pleasssss​

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

plzz answer fasttttt​

PLEASE HELP LOOOOOOOKKKKKKKK ATT SS

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

b. What does the slope represent in this problem?

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

e. What is the equation that represents the line?

Thank you.

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

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plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helpppppppppppppp

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

I’ll mark as brainliest!!!

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