Assignment Instructions: Answer the following questions. Remember to show all relevant work and reasoning. 1. Let A, B, and C be sets. Use the already established formula that for any two sets S, and S2, |S1 U S2| = |Si|+|S2| – |Sin S2| to establish that |AUBUC|=|A|+|B|+ |C| – |AN B| – |AnC| – |BnC|+|ANBNC| Hint: Group two of the sets together to think of them as one set. 2. Now that you have established a cardinal number formula for three sets. Use it to establish a cardinal number formula for four sets A, B, C, and D. 3. Using the original two set cardinal number formula, show that |A = |U| – |A|.

Q: (a) Let A = {1, 4, 6, 7, 8} and B= (4, 5, 6, 8} Find each of the following: i) ANB i) P(AN B) where…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Let the universal set be the set R of all real numbers and let A={x€R|-2<x<2} and B= {xeR|-3<x<0}…

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Q: 10. Let A = {1, 3, 5, 7, 9}, B = {3,6, 9}, and C = {2, 4, 6, 8}. Find each of the following: a. AUB…

A: 10. Given A=1,3,5,7,9, B=3,6,9 and C=2,4,6,8 find a. A∪B   b. A∩B  c.A∪C   d. A∩C   e.A-B   f.B-A…

Q: |a|, called the of a, represents the distance from on the number line. to

A: It is known that a represents the absolute value if a.

Q: For each of the statements below here, decide whether the statement is true or false and prove your…

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Q: QUESTION 5 Which of the following represents the correct interval notation for the solution set of…

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Q: Construct the set S+T in the cases shown in Figs. (a) and (b). a Sb Figure (a) b a b Figure (b)

A: a) Given  S=(x,0)|a≤x≤b and T=(0,y)|c≤y≤d. So S+T is given by  S+T=x+y|x∈S and y∈T…

Q: BC eD AD EC e Gwen Prove <A CE Statements Reasons

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Q: (d) D= {n €Z:n −3} (e) E = {}\{}

A: Here we have to find the set D and E in list form.

Q: Evaluate: 4+(r–3)? O a. itan 1 +c 1 1-3 4 O b. none of the choices O C. tan-1 I–3 +c 4 O d. 3 tan…

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Q: Use symmetry to evaluate the followingintegrals.

A: The given integral is, ∫-22x3-4xx2+1dx The function is f(x)=x3-4xx2+1 When function f(x) is…

Q: Let A = {2, y, 6} and B = {x, 4, z}. which of the following are relation from B into A O a. R = {(2,…

A: We have to find that relation

Q: Rewrite the following sets as simply as possible. a. Øu {0} b. {0}-Ø c. P({0}) - Ø d. Øn {0} e.…

A: We need to rewrite the following sets as simple as possible.

Q: Q 4: Let A=2 -3 2 4 Find AB, AT? and let BD 14

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Q: L e - cos 4tdt

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Q: For set A, B and C,(A U C)n[(A n B)U(C n B)]=A n B. Cite a property from Theorem 6.2.2 for every…

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Q: Let the universal set be the set R of all real numbers and let A={xe R|-2<x<2} and B= {x e IR |-3<x…

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Q: Use any method you choose to show that An (B UC) = A U B n C, when A, B, and C are sets.

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Q: Q14A. Define the sets A, B, C, and D as follows: A = {-3, 1, 6, 7, 10} B = {-10, -5, 1, 4, 6} C =…

A: The given problem is to find the intersection of sets B and D with the given defined sets A,B,C,D.

Q: Use the following to answer questions 21 and 22. 2 0 -2 If X = and Y = -3 4 3 5)- Find 3|X|+ 12 Find…

A: The definitins i have provided their in examples which i have used

Q: Q15A. Define the sets A, B, C, and D as follows: A = {y EZ:2 < y ≤ 9 and y is odd}. B = {1, 4, 6} C…

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Q: E. Prove or disprove: If A, B, and C are sets, then A x (B - C) = (A × B) – (A × C).

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Q: A.) Shiela performed a number trick to Bryan. She let Bryan pick a number divisible by two. She then…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

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Q: -1 5 A = [ 0 2 10 1. 8. 9. 7

A: We have to find determinant first.

Q: iv C = {1,2, 3} v How many elements are in the powerset of N = {1,2, 3,... ,n} for some n E N?

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