Let A, B, and C be sets in a universal set U. We are given n(U) = 66, n(A) = 39, n(B) = 37, n(C) = 33, n(A ∩ B) = 21, n(A ∩ C) = 20, n(B ∩ C) = 21, n(A ∩ B ∩ CC) = 8. Find the following values. (a)    n((A ∪ B ∪ C)C) (b)    n(AC ∩ BC ∩ C)

Q: If A and B are finite sets, then A ∪ B is also a finite set

A: Let A and B are finite sets. We need to show that , A ∪ B is also finite set. case 1) If A = B = ϕ A…

Q: (3) For sets A, B, and C in some universal set U, prove or disprove the following. (a) AnC = B nC =A…

A: Explanation A and B:

Q: Let A and B be subsets of a universal set U and suppose n(U) = 300, n(A) = 150, n(B) = 120, and n(A…

A: Please see the below explanation.

Q: 2. Classify each set as closed, open, or neither. Justify your answer. A= {-+:nEN} E. 1-:] [0, 1)

A:

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A: We have solve the set true and false

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A:

Q: 1. Let A, B and C be the subsets of U. Then prove that (A – B) - (B - C) = A-B by using laws of sets

A: Using properties of set theory

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A:

Q: Prove that if A and B are sets, then P(A) U P (B) C P(AUB).

A:

Q: (3) For sets A, B, and C in some universal set U, prove or disprove the following. (a) AnC = B nc =…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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A:

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A:

Q: if A ⊆ B and C ⊆ B^c , then A ∩ C = ∅.

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Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

A:

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A: The solution is as shown below

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Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if*

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Q: 2. Given the following sets, where U is the universal set, and A, B and C are three sets in the…

A:

Q: Let C and D be subsets of a universal set U, then (C ∪ D) ⊆ (C ∩ D).

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Q: A set is not open if its complement is not closed. O True O False

A: To find the given statement is true or false .

Q: Let A, B, and C be sets. Does A- B= A –C imply B = C? If so, prove it. If not, give a…

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Q: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 150, n(B) = 90, and n(A ∩…

A:

Q: 4. Let A and B be sets, prove that P(A)UP(B) C P(AUB).

A:

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if

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Q: 3. Suppose that A is the set of sophomores at your school and B is the set of students in discrete…

A:

Q: 2. Let C and D be subsets of a universal set U, then 2, (C ∩ D) ⊆ (C4D).

A: False

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A: Given Information -  U is the set of all restaurants in Los Angeles B is the set of barbecue…

Q: Prove or disprove: For all sets A,B and C: (A-B)-C = A-(BUC).

A:

Q: 1. For each of these pairs of sets, determine whether the first is a subset of the second, the…

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Q: If A, B, and C are sets such that A ∩ B ≠ Ø and B ∩ C ≠ Ø, then A ∩ C ≠ Ø

A:

Q: The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. Alabama Arkansas…

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Q: Let A be a finit set and let |p(A)|=n. Let B = A U {x} for some x∉B, How many subsets does B have…

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Q: Which of the following is true for any set A?

A: HERE FOR TRUE SENTENCE FOR ANY SET A . EMPTY SET IS  SUBSET OF ANY SET

Q: Show that if A and B are sets with A ⊆ B, then a) A ∪ B = B. b) A ∩ B = A.

A:

Q: 3. Suppose that A is the set of sophomores at your school and B is the set of students in discrete…

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Q: , and C be subsets of a universal set U and suppose n(U) = 200, n(A) = 26, n(B) = 28, n(C) = 32, n(A…

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A:

Q: Let A and B be subsets of a universal set U and suppose n(U) = 300, n(A) = 150, n(B) = 120, and n(A…

A: We have given the following n(U) = 300, n(A) = 150, n(B) = 120, and n(A ∩ B) = 60.

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Q: Show that if A and B are finite sets, then A ∪ B is a finite set.

A:

Q: Let U be a universal set, and suppose A and B are subsets of U. (a) How are (x ∈A →x ∈B) and (x…

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A: Cardinality of a power set

Q: Let A and B be sets. Define precisely (but concisely) what it means for A to be a subset of B

A: Let, A and B be setswhat it means for A to be a subset of B.

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.