Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N B) = 80. Compute: %3D (a) n(ACn B) (b) n(B) (c) 미ACN B9

Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

Q: The set S = {x | x is a continent}. A. S = {N. America, S. America, Europe, Asia, Africa, Australia,…

A: Given:  ( The set S = {x | x is a continent}  Then write the set S

Q: 7. Show that if S x T is a closed subset of R?, then S and T are closed subsets of R.

A:

Q: Can a set and its complement be both dense in R? Can a set and its complement be both nowhere dense…

A:

Q: Let A = {w, x, y, z} and B = {a, b}. Use the set roster notation to write each of the following…

A:

Q: Explain whether each of the following sets is countable or uncountable.  A= {x∈Q|−100≤x≤100}…

A: A= {x∈Q|−100≤x≤100} This is the subset of Raitional Number. And we know that Rational number Q is…

Q: For all sets A B and c, of CAXC)- CBrC)# Ø, then A-B#¢.

A:

Q: For the set B = {a,b, c, d, e} list all of the subsets having exactly two elements. O{b, c, d} O{a,…

A: We need to select the subsets of the set B={a, b, c, d, e} having exactly two elements (cardinality…

Q: Assume that the set S has 14 elements. How many subsets of S have at most 4 elements

A: At most 4 means 4 or less.  Let us denote X=number of elements

Q: How many proper subsets does the set T={h,f,k} have

A: A set is given by, T = h, f, k. The objective is to find the number of proper subsets the T have.

Q: The following table shows the total student enrollment at a certain university for the years 2001…

A: ∵ Given that Year Enrollment 2001 5621 2002 5687 2003 5805 2004 5783 2005 5758

Q: The following table shows the results of a survey of authors by a fictitious publishing company.…

A:

Q: 7. Find an indexed collection {A„}nɛ N oftwo distinct sets (that is, no two sets are equal…

A: We have to find an indexed collection Ann∈ℕ of two distinct sets satisfying the condition ∩n=1∞An=0…

Q: Let A (k,s), t.en the power set of A is:

A: Set of all subsets of A is called power set of A.

Q: 9) Find the power set of each of these sets, where X, y are distinct elements: (a) {x, y} (b) {x, y,…

A:

Q: . Let A and B be two connected subset

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

Q: For a poset with the following Hasse diagram, consider the set {b, e, f}. The least upper bound of…

A: using the concept of upper bound least upper bound in hasse diagram...

Q: The following table shows the number of new (single-unit) houses started, in thousands, in the…

A:

Q: Consider the set C={Ø,{Ø},{Ø,{Ø}}}. How many elements are there in the power set P(C)? *

A:

Q: 5. Give an example of a collection (A,, of sets with the properties that: (a) A, # Ø for each i> 1,…

A:

Q: Let R = Zg, and let N = R³. Determine whether or not X = {(4, 5, 4), (4, 5, 2), (2, 2, 3)} is a free…

A: It is given that,  R = ℤ8  and  N = R3. We have to determine that whether the set,  X = 4, 5, 4, 4,…

Q: Show every possible 1-1 correspondence between the following sets. {A,B} and {a,b}

A: The solution are next step is

Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

A:

Q: 2. Write the following sets in roster notation. (a) {r|x € N, x -3} (c) {r |x € N, –2 < x < 6}

A: Given we have given the following sets (a) x x∈ℕ , x≤-8 (b) x x∈ℤ, x≥-3 (c) x x∈ℕ,-2≤x&lt;6 we have…

Q: Let E be a nonempty subset of an ordered set; suppose a is a lower bound of E and B is an upper…

A: Let X be a non empty set. Let a∈X. Then a is said to be a lower bound of the set X if a≤x for all…

Q: Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - U B, = N(A – B„,).…

A: Suppose that A is a set and Bnn∈I is an indexed family of sets. Then we have to prove that…

Q: Finish labeling the number of elements in the regions in the Venn diagram shown to the right, where…

A: Given information :

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: Let S and T be subsets of the universal set U. Use the Vern diagram on the right and the given data…

A: here given S and T be subsets of the universal set U

Q: Determine the number of distinct proper subsets for the given set {c, a, v, e}.

A:

Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: Consider the given word TORTOISE. The objective is to count the number of arrangements of this word:…

Q: 12. Find two sets A and B such that A e B and A B.

A: 12.Find two sets A and B such that A∈B and A⊑B

Q: Consider the set A = {xy : x ∈ N, y ∈ N} = {1, 2, 22, 23, 24, ...., 3, 32, 33, 34,......, 4, 42, 43,…

A:

Q: Finish labeling the number of elements in the regions in the Venn diagram shown to the right, where…

A: Total number of elements in universal set, n(U)=100 Total number of elements in subset A, n(A)=30…

Q: a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at…

A: Given: It is given that suppose that A is the set of sophomores at your school and B is the set of…

Q: The following table shows the results of a survey of authors by a fictitious publishing company.…

A: Part (a) Given data is Where set of successful authors represent by 'C', set of unsuccessful…

Q: Let A be a well-ordered set, then every subset of A is not well-ordered

A:

Q: The following table shows the results of a survey of authors by a fictitious publishing company.…

A: Given:   New Authors (N) Established Authors (E) Total Successful (C) 6 24 30 Unsuccessful…

Q: Enumerate

A: The set S contains 5 elements, Number of subset = 25 = 32

Q: The sets A and B have 6 and 9 elements respectively, such that A is proper subset B , then the total…

A: Given that set A and set B have 6 and 9 respectively. Now that A is a proper subset of B which means…

Q: If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements,…

A: Given that n(X ∪ Y)= 50  n(X)= 28 and n(Y)=32  We have to find n(X ∩ Y )= ?

Q: For every set A, {Ø} C A.

A: We use the definition of an empty set and subset of a set to answer the given question.

Q: Define the sets D = In E N} n+1 Prove whether D is finite, countable, or uncountable?

A:

Q: (4) How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all…

A:

Q: Given a set A of n elements, in how many ways can you find two set P,Q ⊆ A (not necessarily…

A: Given set of  elements we need to find number ways in which A can be written as union of two…

Q: (c) Show that the set {r EN | x² % 4 = 1} is equal to the set {EN | x² % 8 = 1}.

A: Two sets are said to be equal if the number of elements in both the sets are equal. Now, we have one…

Q: Let S be a set of n elements. Find the number of distinct subsets of S.

A: Given: Let S be a set of n elements.

Q: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C. If B is 4…

A: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C.

Q: Show that the union of two sets, each of measure zero, has measure zero

A: