Let S = {1, 2, 3, 4, 5, 6, 7, 8}. (a) How many nonempty subsets of S are there? (b) How many subsets B of S satisfy the property that {1, 8} ⊆ B? How many subsets B of S satisfy the property that {1, 8} ∩ B = ∅? (How are subsets in the first question related to subsets in the second question?) (c) How many sets B satisfy the properties that B ⊆ S and |S| = 3? (d) How many subsets of S are there with exactly three elements, at most one of which is even?

Q: A bag contains four red marbles, three green ones, one lavender one, three yellows, and two orange…

A: Given,no.of red marbles=4no.of green mables=3no.of lavender marbles=1no.of yellow marbles=3no.of…

Q: Which of the following statements is correct about 2 1.13 2 2 the set S = Select one: 3 S spans 3 3…

A:

Q: Let U =  {2, 3, 4, 5, 6, 7, 8, 9},   A =  {3, 5, 7},   B =  {2, 3, 6, 9},  and C =  {2, 4, 8}.…

A: Given U = {2, 3, 4, 5, 6, 7, 8, 9},   A = {3, 5, 7}, B = {2, 3, 6, 9}, and C ={2, 4, 8}. Find  (A ∪…

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

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Q: Ex: Let X₂ [1,2,3,4,5]. I. [0,X, [1], 82.3, 81.23], Y. [3,4,5,6,73 andl T₁: [0, X, [4], [4,633 if A:…

A:

Q: Which of the following sets spans Rº 3 None O {(1,2,3),(0,0,0)(-2,1,0)} {(2, – 1,2),(4,1,3),(2,2,1)}…

A: vectors span R3 means that some combination of the vectors can take up all of the space in R3.

Q: Let U = {3, 4, 5, 6, 7, 8, 9, 10},  A = {4, 6, 8},  B = {3, 4, 7, 10}, and C = {3, 5, 7} . Find the…

A: It is given, U= {3,4,5,6,7,8,9,10}.

Q: A multiset is a collection of objects, just like a set, but can contain an object more than once…

A:

Q: Which of the following sets spans R? O {(3,0,-2)} O (3,0,-2),(0,0,0)} O ((3,0,-2).(5,1,0).(0,-1,1)}…

A:

Q: Express the set in roster form. The set of natural numbers between 14 and 182

A: the set of natural numbers between 14 and 182

Q: Subset: Let X = { 10,20,20,20, 30, 40, 10 } and Y = { 20, 40 }.  Is Y the subset or proper subset of…

A: Given  X = { 10,20,20,20, 30, 40, 10 } Y = { 20, 40 }  We need to find whether Y is subset or proper…

Q: Which of the following sets spans IR³? O ((0,1,-1),(0,0,0) O {(-3,0,2).,(5,1,0),(0,1,-1)} {(0,1,-1)}…

A:

Q: Let A = {1,2} and B = {3, 4}. (a) Find A x B (b) How many subsets Ax B of size 2 are there? List…

A: Given that A= {1, 2} and B= {3, 4}A x B is the cartesian product

Q: Which of the following statements is correct about the set -3 6 -898) 2 -4 -2 S = Select one: O O O…

A: There is set S given. One has to check whether S spans the vector 333 and vector space R3 or not.…

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Which of the following sets spans R³? {(0,1,-1)} None of these O {(0,1,-1).(0,0,0)} O…

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Q: In how many ways can we compose a word of 3 letters from the set {X, Y, Z, F, S} if repetition is…

A: Given, Letter set  = {X, Y, Z, F, S}  words should be 3 letters,

Q: Let A = Z*, B = {n Ez,0sns 100}, C = {100, 200, 300}. Evaluate if tl statements are True. Explain…

A: Given   B=n∈Z, 0≤n≤100  , A=Z+ and C=100,200,300 16. B⊆A Since every element of B lies in A. But…

Q: Which of the following sets is (are) proper subsets(s) of the set of the multiples of 5? Choose one…

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Q: Using the fact that "a countable union of countable sets is countable", show that the statement that…

A: Please see the below picture for detailed solution.

Q: {5}⊂{1, 3, 5, 7, 9,...} true or false

A:

Q: {x|x<2} is (-00,2) in set notation form. O True

A: Given that: {x|x&lt;2}

Q: Find P(C1)  l. Find P(V4)  m. Find P(C1 ∩∩ V4)

A: As per guidelines we are allowed to solve maximum of 3 sub parts If you need help with other…

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.

Q: Use the roster method to describe the elements of the following sets. ([-4,6) n (-3, 11)) nZ =…

A: The given sets,The objective is to describe the elements in the given set by roster form.

Q: | Let A = P({1,{1}}}, B = P({0,1}), and C = P({0,1}) where P(S) is the power set of S. Find the…

A: (1){{0},{0,1}}(2){ϕ,{1},{{1}},{1,{1}},{0},{0,1}}(3)ϕ(4) Refer to explanation part below.   If you…

Q: Which of the following sets spans R³? None of these O {(0,1,-1)} O {(0,1,-1),(0,0,0)} O…

A:

Q: Let A = {1,3} and B = {2,4}. (a) Draw a picture of the set A × B. (b) Compute P(A × B).

A:

Q: If A = {1} and B = {1, 2, 3, 4, 5} , then which of the following is(are) true? Choose one answer and…

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Q: Let A = {1,2}. List the elements of A x P(A).

A: Note: We will be solving only Q.8 as asked.Given that .We need to find .The power set of a set…

Q: Express the set in roster form. B= {x| xEN and x is even) Choose the correct answer below. O A. B=…

A: Please refer the attached image for complete solution.

Q: S=(n is an integer and 0 ≤ n ≤ 9), L = (2,3,7,9), M = (2,4,7,8), and N = (0,2,5,8,9).Find the set (L…

A: