Homework: Determined whether the following sets are open or closed in (IR", ||. |I): 1) [a , b1] × .…× [an , bn] ; where a; ,b; E R; Vi = 1,...,n. 2) S = {(x1,.. , Xn) : x > 0} ; USt , St. %3D 3) Any finite set in (R, | |). 4) The set QC in (R,| · |).

Q: Let 4, B, and C be sets. Show that а) (А — В) — С СA-C. b) (A — C) n (С- В) — 0.

A: It can be solved by the set theory

Q: Let U=(1, 2, 3, 4, 5, 6, 7), A=(1, 3, 5, 7), and B=(2, 5, 7). Find the set AnB AnB= (Use ascending…

A: Note: The complement of set A is defined as a set that contains the elements present in the…

Q: ) (AO B) © (A^ B) = A UB.

A: Introduction :

Q: Let S = {(r.y) R²: (x-1)² + y² ≤4 and y> √3}. Question a. Find the interior, exterior and boundary…

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Q: Complete the proof: If A≤B and B≤C, then ACCn(transitive property for set in inclusion) Need to…

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Q: Show that the sets [0,1] and (0, 1) are equinumerous 7.

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Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (B-C).

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Q: P(X=x) 0,10 0,20 0,30 0,40 P(3 < X S4 )= ??? O A) 0,10 O B) 0,40 C) 0,30 O D) 0,50 XN34 5

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Q: 2) Let R' real numbers, define = x,Y1 + 3x2y; + 5x3y3 for x = (x, X2, X3) and y (y,Yz, Y3). Is…

A: Given x=x1,x2,x3, y=y1,y2,y3 in ℝ3. Define x,y=x1y1+3x2y2+5x3y3

Q: Let f AB, prove the following: (a) if S, T are subsets of A, then f(SNT) ≤ f(S) nf(T); (b) if U, V…

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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 is true for all sets S and T? Select one: O A. SOT SOT B. SOT SUT C. SUT SOT…

A: see below the answer and explanation

Q: Find the value of a for which V= 2 a 5 is in the set a= H = span -5 3 5 0 -3 -5 0 -2

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Q: Theorem: let S₁, S₂ be the collection of sets D (US) U (US). = US. SES, VS₂

A: Solution: Let S1  and S2  be  the  collection of sets.We  have  to show  that  ∪S∈S1S∪∪ sS∈S2=∪…

Q: Construct RM so that it bisects &RAT Construct HG || EF.

A: Given quation there are two subpart . so in first subpart ask that angle bisect here first i define…

Q: Which of the following is NOT always true for sets A and B such that AC B? A. AnB = A C. BU (A - B)…

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Q: Which of the following set is consistent? Select one: O i. None of these O ii. (A&~(BVA) } O i. {J>…

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Q: When is S \ T = T \ S for sets S, T? Give an example

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Q: For the four pairs of sets below, determine whether or not they are equipollent. i.) {2, 5, 10} and…

A: We have to find the equipollnt sets from the given pair of four sets.

Q: In this task there are two situations: one dealing with counting toothpicks and the other dealing…

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Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: True or False?

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Q: 5) Again let Universe U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Let S = {0, 1, 2}, T = {1,4}, R = {2, 4,…

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Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B) n (A x C)

A: we have to prove the lemma .

Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

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Q: Consider (Power set of R, c). Let B= {{3},N,Z,Q,R-Q), then Sup(B)= %3D O a. R O b. Q O c. R-Q Od.…

A: Consider Power set of R, ⊆ Let B=3, N, Z, Q, R-Q then SupB is the set S∈Power set of R such that…

Q: and n 12/22 -42 Z+6z Z722+2 2ナ z2, 4z+3

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Q: 5 7. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C X such that…

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Q: a) What is the role of a and k in y = alx|+k?

A: Answered first question as per our company guidelines. Second question is incorrect please repost…

Q: Q7 IF THE MAPPING BETWE EN I AND ã is: WHERE A 1s A 2x2 MATCIX OF CONSTA TS., AND T a) GHOW 2

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Q: For the poset, R = ( { 1, 2, 3, 5, 10, 15, 20, 25, 30, 35, 50, 70 }, | ):   Draw the Hasse digrams…

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Q: (f) Let A, B and C be three sets. Prove by contradiction that if An BC C and r E B, then x ¢ A - C.

A: Let A, B and C be the three sets. Prove that, A∩B⊆C, and x∈B, then x∉A-C

Q: Let: U={a,b, c,d, e, f, g} and to A= {a,b,c,d} B={C,d, e, f} C={a, e,g} %3D Find the set or…

A: Solution: From the given information,

Q: Assume X = (1,3,5,7}, Y = (1,9,25,49)} and F(x) = x2, such that F:X Y. Then the following is true…

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Q: The shaded regions below represent the set {(x, y) | P(x, y)}. This means every point in the shaded…

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Q: 4 The set {# € R : \# + 3| + z > 2} equals Select one O a (-0, -3) U|-,00). O b.(-3, 0). O d none of…

A: If we have x&gt;a then it can be written as: x&lt;-a or x&gt;a Now, we have x∈ℝ: x+3+x&gt;2 Now,…

Q: Let A = [3, 8], and B= (-00, 4). Choose sets that are infinite and uncountable. O P(ANN) O P(AnQ) O…

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Q: Q25] Decide if the following domains are simply connected or not. Write your reasoning? a) b)

A: A domain D is said to be simply connected domain if it is path connected where one can shrink any…

Q: LetZ:Nlo,1), Find p(IZI>-I |121< 2)

A: Given Z~N0,1