Let A and B be sets. Show that A∪(A∩B) =A using a traditional verbal proof, a series of equalities that can be read forward and backward, or a membership table.

Q: Let the Universal Set, S, have 146 elements. A and B are subsets of S. Set A contains 84 elements…

A: Given that universal Set  S have 146 elements. Set A contains 84 elements. Set B contains 25…

Q: (c) iii) Common elements of two sets A and B are denoted by: (a) AUB ANB (c) ACB (d) AB ins

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Q: Consider the following sets: U = {2, 3, 4, 6, 8, 9, 10, 12, 14, %3D 15} |А%3D {3, 6, 9, 12, 15} В…

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Q: a. Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and…

A: # we are entitled to solve one question at a time. Please resubmit the other questions of you wish…

Q: Use set notation​ (braces) to write the members of the following​ set, or state that the set has no…

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Q: 5. Write the following sets using set -builder form: А - (5, 9, 13, 17) b. В-(1/65, 1/50, 1/37,…

A: 5. a. Consider the set A=5,9,13,17. The elements of the above set are obtained as follows. The 1st…

Q: H={b ∣ b ∈ N and 124 < b ≤ 130 } H= { b ∣ b ∈ ℕ and 124 < b ≤ 130} Use the roster method to list…

A: Given the set is  H= { b ∣ b ∈ ℕ and 124 &lt; b ≤ 130} To write the roster method to list the…

Q: Use an element argument to prove the statement. (Assume that all sets are subsets of a universal set…

A: Consider the provided question, We have to show that,

Q: If U is the set of all multiples of 3 less than 20, and M={3,12,18}, find Mc (the complement of M).…

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Q: Let A and B be sets. Show that A∪(A∩B) =A using a traditional verbal proof, a series of equalities…

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Q: How would a mathematician say: “Take the set {s,u} and give it the name G” Let D = {u,j}. Is j a…

A: 1. Let, G=s,u 2. Consider a set D=u,j. A set X is a subset of another set Y. If all the elements of…

Q: Let the Universal Set, S, have 89 elements. A and B are subsets of S. Set A contains 37 elements and…

A: Given that :  S have 89 elements A have 37 elements B have 30 elements A and B have 25 elements in…

Q: Is the set named empty, finite, or infinite? (a) L = {points on a line} emptyfinite infinite (b)…

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Q: Prove for all sets A,B,C if A⊆B, then C−B⊆C−A.

A: Three sets A, B, C are given such that- A⊂B To show- C-B⊂C-A

Q: State whether each of the following statement is true or false. Justify your answer.(i) { 2, 3, 4, 5…

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Q: Are these sets finite or infinite? a) V = {vowels} {a,e,i,o,u} b) N = {natural numbers}

A: If a set has unlimited number of elements, then it is infinite and if it has countable elements,…

Q: Given the folllowing sets (where U represents the Universal set), determine the result of the…

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Q: Let A, B, and C be finite sets, with ACBC C and n(B) = 7. (a) What are the possible values of n(A)?…

A: Given:  A, B, and C are finite sets. A ⊂ B ⊆ C and n(B) = 7. Subset and subset notations: A subset…

Q: Determine whether each of the following  statements are True or False and why:…

A: 1) False. A set A is a subset of a set B if and only if every element in A is in B.For any sets A…

Q: Decide if the given statement is true or false. If it is false, give the reason. (7, 9, 5) C {7, 5,…

A: We need to find correct option for proper subset.

Q: a. Are Aj and A, mutually exclusive? Explain. b. Compute P(A, N B) and P(A, N B).

A: Given :  Our claim is to answer the following :  A) Are A1 and A2 mutually exclusive&gt; B) Compute…

Q: Use an element argument to prove the statement. (Assume that all sets are subsets of a universal set…

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Q: 2. Using the set-roster notation. а. Let A = {1,2,3}, B = {3,1,2}, and C = {1,1,2,3,3,3,3}. What are…

A: 2. (a) Given that A=1,2,3,B=3,1,2,C=1,1,2,3,3,3,3 Now, set A,B,C have exactly 3 element 1,2,3. Set…

Q: Let S = {Aylesbury, Manchester United, Southend, Sheppey United, Liverpool, Golden Arrows, Witbank…

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Q: lve an example to Show "arbi ombitrany union of again open s tue result: true open sets is for…

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Q: Determine whether the following sets are equivalent, equal, or disjoint sets.  1.) B = {red,…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: Let the Universal Set, S, have 141 elements. A and B are subsets of S. Set A contains 96 elements…

A: Universal set S contains 141 elements. Set A contains 96 elements. Set B contains 57 elements. Total…

Q: Answer the remaining questions about set theory and probability theory.   d) Give an informal…

A: Given  X⊂ Y  Y⊂ X

Q: Consider the setsφ, A = { 1, 3 }, B = {1, 5, 9},                               C = {1, 3, 5, 7,…

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Q: Use element argument method to prove that if A and B are sets such that P(A) ≤ P(B), then A ≤ B,…

A: I just used the definition  Of power set and subset of set

Q: The table shows some trees that are in two city parks. Let U be the smallest possible set that…

A: The set Re defines the set of trees in Riverside Park and set S defines the set of trees on Sleepy…

Q: Match the following term with the appropriate description​ A-F below. Assume A and B are sets.   The…

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Q: Decide if the given statement is true or false. If it is false, give the reason. (2, 9, 6) C {2, 6,…

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Q: Give a proof by contradiction to show if C and D are sets, then C ∩ (D ∩ C’) = {}.

A: Given C and D are sets.

Q: The results of a survey taken by a bank in a​ medium-sized town are shown in the table. The survey…

A: Intersection of column B and row Y is 2.

Q: Which of the following statements is true OA. For all sets A, B and C, A- (B –C) = (A - B) -C- O B.…

A: Option B and E are correct.

Q: Match the term with the appropriate description. Assume A and B are sets.   the difference of A and…

A: Set difference denoted as A - B

Q: Let the Universal Set, S, have 101 elements. A and B are subsets of S. Set A contains 59 elements…

A: It is given that,  set A contain 59 elements, n(A) =59 Set B contain 38 elements, n(B) =38 Set A and…

Q: Exercise 1.5.5. (a) Why is A- A for every set A? (b) Given sets A and B, explain why A~ B is…

A: (a) To prove that, A ~ A for every set A.

Q: b. Use the Sum Rule for two sets to show that |A UBUC| = |A| + \B| + \C| – |A U B| - |A U C| – |B U…

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Q: point the step in the argument that is not valid and explain why ? Theorum: For all sets A,B   A’∪B’…

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Q: Find a counterexample to show that the statement is false. Assume all sets are subsets of a…

A: We have to show that given relations is False.

Q: Determine whether the following pair of sets is equivalent. Justify your answer. {a, b, c, d,.., z}…

A: Given the two set  {a , b, c ,d ,........, z } and  {1 ,2 ,3 , 4 ,........ ,26} We need to check…

Q: Use roster form to write the elements of the following set, or state that the set has no elements.…

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Q: Write the following in set-builder notation H={2,4,6,8} I={1,3,5,....} J={1,2,3,4,6,12}…

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Q: Let A = { 0, 2, 4, 6, 8 } a. Determine whether each of the following is true or false: i. ii. 2 € A.…

A: We have to answer true or false and the description of A and possible lists of A.

Q: Choose an n and m that satisfies the following statement

A: We need an example such that  n = m! Take n = 24 and m = 4  Then m! = 4! = 24 Hence , n = m!

Q: Is the set named empty, finite, or infinite? a) N = {counting numbers} b) V {vowels} {points in the…

A: The empty set (or null set) is a set that has no members.   Finite sets are the sets having a…

Q: Proof that (A ∩ C) − B ⊆ (A − B) ∩ (C − B) Consider the sentences in the following scrambled list.…

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Q: Consider the sets to answer the following questions attached: A = {a, b, c, d, e, f, h, j} B = {a,…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.