5. Let A, B, C be following sets: A = {x € Z* \x is multiple of 3 and x < 20} B = {x € Z* \x is even and x < 15} C = {x € Z* ]x is odd and x < 20} Find cardinalities of following sets: |C| = a) |A| = b) JANB| = c) |ANC) = d) |BNC| = e) JAUB| = f) |AUC| = 9) |BUC| = |B| =

Q: 14) A subset of topological space X is dense in X iffA a) intersect every set c) intersect every…

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Q: ieN (4 For each nEN, let A, = {-2n,0,2n}. (a) UA; = (b) NA: = ieN ieN

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Q: Let U = R be the universal set and A = [1,3], B = (-∞,6], C = (-4,0). a) AUB b) BnC c) A-C d) BC

A: Let  be the universal set and  Then we have to answer the following...

Q: 4- A subset [a, b] R is compact set in: a- (R, Td), b- (R, T), c-Both (R, Tu) and (R, T₁) d- No one.…

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

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A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

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A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

Q: 14. Assume that R is a well-founded relation, x is a regular infinite cardinal, and card{x | xRy} <x…

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Q: 11.0, Prove that the interior of the interin of a set is equal to the interies of that set

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Q: 3. Let R be the universal set and D = (-7,4], E = (0,8), F = {r: r ≤ 10, r € R} be the subsets of X.…

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Q: Let Gbe an open set in R". Two points x, y e G are said to be equivalent if they can be joined by a…

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

Q: ind the cardinality of A when A = {x €Z : -2 <æ < 100} A) 103 B) 100 (c) 102 (D) 99

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Q: O P(0) = {0} © P(A°)\ {0} C P(A)°

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 16. consider the following sets: U={-5,-4,-3,-2,-1,0,1,2,3,4,5}; A={x: x^2=25} ;B={-5,0,1,2,3,4,5};…

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Q: 2. Let U = {0,1,2,3,4,5,6,7,8,9,10); a) How many subsets will A have? b) Lis only the elements of…

A: as per Bartleyby rules we have to answer only 3 subparts.

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Q: . List all the elements of {x ∈ Z : x^2 − 2 = 0}.   2. Find the cardinality of the set B = {n ∈ N…

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Q: let Aand B be b ounded setsof real numbersprove that supCA+B) =SuPAtspanB

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Q: Sets B and C are subsets of the universal set U. These sets are defined as follows. U={f,k,m, x,y }…

A: It is given that: U=f,k,m,x,y,B=k,y,C=f,k,m Therefore the complementary sets of B and C are:…

Q: prove that i } X is a Coun table set and P: X>Y is asurjecbive then Y is Countable

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Q: A:={x∈ℤ+| 1≤x<11 and (∃a∈ℤ+, a^2≡x(mod11))} B:={x∈ℤ+| 1≤x<13 and (∃b∈ℤ+, b^2≡x(mod13))} a) Specify…

A: Given A:=x∈ℤ+| 1≤x&lt;11 and ∃ a∈ℤ+,a2≡xmod11B:=x∈ℤ+| 1≤x&lt;13 and ∃ b∈ℤ+,b2≡xmod13

Q: If a universal set has 500 elements, n(a)= 240, n(AUB) = 400, n(An B) = 55, what is n(B')?

A: Total number of elements = n(U) = 500n(A) = 240n(A  B) = 400n(AB) = 55We have to find n(B').

Q: A = {x € Z: xis even} {91'SI'ZI'6'S'E} = 5 23242+3 2184 21+ 122198 th

A: Given,            To find the value of

Q: ieN 5. (a) Uli,i+ 1]= (b) Nli, ieN ieN 6. (a) | Iro.i +11=

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Q: Let A and B be the following sets: A = {m ∈ Z | m = a^2 +3 for some odd integer a}, B = {n ∈ Z | n…

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Q: 1) Let f: A ->B with C1 C C2C A and Dic D,CB Which is true? a) f(C) c f(C2) OR b) f(C2) c f(C:) (i)…

A: Given: i) To prove that answer is correct. ii) To give a counterexample to show that the set…

Q: ☺ Let (u,Ue...,un) be a lineorly ndependent list. Which True Statement? is a has --- a non-zero…

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Q: A. Let A = {x ∈ N | x = y^2 such that y ∈ N and 2 ≤ y ≤ 7}     B = {x ∈ N | x = 5y, such that y ∈ N…

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Q: 3) Let S be o st defined os follow s: 05 Deter mire ue ther S is o con vea set or not.

A: We have,  The set C is said to be convex set if for any u,v∈C, the point tu+1-tv∈C for all t∈0,1…

Q: I) We know that -5,-4,-3,-2,-1? and IN are well-ordered sets with respect to the trivial ordering.…

A: Solution: Given the sets -5,-4,-3,-2,-1 and ℕ are well-ordered with respect to the trivial ordering.…

Q: Determine the membership and the cardinality of each of the sets given? a) A = {x | xN and x…

A: Note: According to Bartleby we have to answer only the first three subparts of the given question…

Q: 23. Find the power set of each of these sets, where a and b are distinct elements. a) {a} b) {a, b}…

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Q: the letters in the word COMPUTER be arranged if the

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Q: Let A, B, and C are three sets, prove that B×(AnC)=(B× A)^(B×C)

A: Given 3 sets A, B and C. We have to prove that B×A∩C=B×A∩B×C. For this, we have to show that…

Q: Let Gbe an open set in R". Two points x, y e G are said to be equivalent if they can be joined by a…

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…