(1) In the universal set U ={1,2,3,4,5} we define the following sets: A ={1,2,3}, B = {3,4}, and C = {5}. Find, using the appropriate notation, the following sets: (a) (AnB)UC (b) (AUB)°NC° (c) A \B

Q: For each category on the next page, identify all those shapes on this page that have all the…

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Q: 11. For sets A and B, define AAB (A\B) U (B\A). Prove that A B if and only if AAB=0. - (a) Let A and…

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Q: For sets A and B, prove that AU (B – A) = B

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Q: 6. Given the universal set U ={x | x e 1, -10 sxS 10} A = {-2, -1, 0, 1, 2, 3 } B = {2, 3, 4, 5, 6,…

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Q: 2. If A = {a,b,c}, B = {1,2,3}, C = {x}, and D = 0, list all of th the following sets. (a) Ax B (c)…

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Q: Let A = (1, 0), B = (0, 1), C = (1, 1), and D = (r, 1). There are 24 orderings of the four points A,…

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Q: 1) Which of the following point sets are in general position? aj {(0, 1), (1,3),(2,5)}, b.) {(0,0),…

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Q: 1. Determine the possible values of a, b and c, such that alb,ac and bif: a = [a, 5, 1], b = [-5, b,…

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Q: 1. Let X be the set of real numbers with the usual pseudometric. Find the derived set and the…

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Q: Exercise 2. Let A, B C R. (a) Prove that AUB = AUB. (b) Prove that ANBCAN B. (c) Find sets A and B…

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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: S Dite Y as b, and Va, îf possi ble. (if not ponible, enter ImporsiBce) V= (9, -24,-13,-14), H,=…

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Q: et A, B, C and D be sets. Prove that (AnB)u(CnD)=(AUC) n(BUC) n(AUD)n(BUD)

A: The set A∪B contains all the elements that are present either in set A or in set B. The set A∩B…

Q: Consider following five sets: I.{ , } { } II. { } III. IV. { , , } V. { , } Find all set(s)…

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Q: 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)…

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Q: Name the set identity that is used to justify each of the identities given (a) (BNC) UBNC=U (b) AU…

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Q: Define the Cartesian product of sets X and Y? How is this Cartesian product denoted?

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Q: 3) Let x = (-1,3,2,-4), and y = (1,0,2,3). Find the following distances || x = || = ? []x - || =?

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Q: 8. Let A = {2, 4} and B = {1, 3, 5} and define relations U, V, and W from A to B as follows: For all…

A: In the given question we have to draw the arrow diagram of the relation U,V and W and we have to…

Q: TO 8a. Place the numbers 4n, -8, 2-3 and 42 in the correct position on the Venn diagram. 8b In the…

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Q: Let K = {A, Ā, A-°, A-o-, A°, A°¯, A°-o}. Show that K is closed under the interior and closure…

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Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B) n (AUC)

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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: Each Venn diagram has sets A, B, and the universal set U. (a) Shade A UB'. Explanation Check B + (b)…

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Q: (m) W ) Given A, Be {sets}, V AC B, A – B= A.

A: Given: A,B∈sets and A⊂B since A⊂B⇒A-B=ϕ we have to prove A-B=A So, these will happen when A=ϕ So,…

Q: Let 4, B, and C be sets. Show that а) (А — В) — С сA-C. b) (А — С) n (С- В) 3D0.

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Q: If the functi ons f and g are given by f = {(1,2),(3,5).(4.1)} g= {(2,3).(5.1).(1.3)}. Find range of…

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.