1. Let the universal set be the set S = {1,2,3,4,5,6,7,8,9,10} and let A= {1,2,3,4,5} , B = {2,4,6} and C = {3,6,9} Find: a. ANB= b. AUB = c. A-B= d. A° = e. P(C) = f. B×C=

Q: Let A, B and C be sets . The proof of (AU (BNC) C AN (BU c) is as follows: Let x E ( Αυ (ΒηC) x E Ā…

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Q: 5. Let S = {a, b, c, d, e, f}, T = {a, c, e, f}, R= {a, c, f}. Find the following sets. (a) SnT (b)…

A: According to our guidelines we can answer three sub-parts and rest can be reposted.

Q: Given the relation R = {(u,t),(v,t),(w,t),(w,u),(w,v)} on a set A = {t,u,v,w}, what is/are the…

A: topic - relation

Q: Let R = {a}, S = {x, y}, and T = {p, q, r}. Find each of the following sets.a. R X (S X T)b. (R X S)…

A: Cartesian product of set A and B is defined as:

Q: 3. Let A, B be nonempty sets and a,b ¢ A, 1,2 ¢ B. Show that if A B, then AU{a, b} ~ BU{1,2}.

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Q: consider Hhe oniver sal set U= {1,2,3, -9 and A = {!2, 3,4.5, 8 ={1.5147}, C= {5,6,7;8.9} {"31 S,…

A: We have to find  the elements by in the set by doing the operations.

Q: Let A, B, and C be sets. 1. Prove: If A C B then ANC C B C. 2. Disprove: If A NCCBNC, then AC B. 3.…

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Q: Let A- (2, 4) and B- (1, 3, 5) and define relations U, v, and W from A to B as followS. For every…

A: Given

Q: Show that the following pairs of sets S and T are equinumerous by finding a specific bijection…

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Q: Which of the following set S is a spans R"? a. S = {(2, 1), (2, 1)} b. S = {(1,2, 3), (3, 2, 1)} c.…

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Q: If c eR and S is a set, define cS be a convex set and suppose c > 0 and d > 0. Prove that cS + dS =…

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Q: 1) For the universal set U and the given sets U = {1,2,3,4,5,6,7,8,9,10}, A= {1,3,5},B = {1,2},C =…

A: The given universal set is                                          U={1, 2, 3, 4, 5, 6, 7, 8, 9,…

Q: Given sets X and Y. For x EX and for y E Y, we form the Cartesian produc X x Y := {(x, y) : x E X, y…

A: Given that: X={-1, 1}Y={-2, 0, 2}

Q: Question 1: Let A = [(0,6) U (7, 12) n(2,9): B= A\ ({1,2, 4} U (3, 5)) and C =BU{11,8}. Give an…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Show every possible 1-1 correspondence between the following sets. {a, b, c} and {1, 2, 3}.

A: Possible 1-1 correspondence between two sets

Q: 2. Given A, B, and C are non-collinear points, draw the following or explain why it is impossible…

A: We have given three points A,B,C  which are non colinear  that  is these three points does not lie…

Q: In the poset represented by the Hasse diagram, consider the set {e, h, i}. The upper bound of this…

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Q: Find the Cartesian Product of the given sets:  With A = {c, d, f} and B = { w, x}, find B x A.

A: A = {c, d, f} and B = {w, x}, B x A = { (w,c), (w,d), (w,f), (x,c), (x,d), (x,f) }

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

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Q: Given sets A and B in a universe U, draw the Venn diagrams of each of these sets. a) A → B = {x ∈ U…

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Q: Given the sets A = {1, 2, 3, 4, 5} and B = {2, 4, 6}, calculate the following sets: i. AU (B N A)…

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Q: (d).Show that the derived set E′E′ of any set EE is closed.

A: To show that derived set E′ of any set E is closed.

Q: Let A, B and C be sets. It is given that AUC= BUC and AnC= BnC. Shơw that A = B.

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Q: Let A, B and C be sets. Prove that  A ⊆ B if and only if A − B = ∅,

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Q: Given the following sets (where U represents the Universal set), identify the correct Venn Diagram…

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Q: Which of the following sets best describes the shaded part of the Venn diagram? (B'AC}UA (CnA) UB Di…

A: Let'do it in two steps. As a first step let's explore:  This is the shaded portion in the diagram…

Q: 1. Construct the set S+T in the cases shown in Figs. (a) and (b). 9 S D Figure (a) Figure (b)

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Q: For any sets A and B, (AU B)

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Q: Let S = {1,2,3,... 18} and define the relation R by xRy if xly. Draw the Hasse diagram for R.

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Q: Let A, Band C be sets. Prove that if A⊆B∪C and A∩B= ∅ then A⊆C.

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Q: 2. Consider the directed line segment from M(2,7) to S(10, -4). Points A, R, and K are on MS. (30 27…

A: Given: Directed line segment from M(2,7) to S(10,-4). Points A,R and K are on MS.

Q: Let Á = ry?a, + x³yzay, Evaluate A. dl along the path y = x2 from a(0,0,2) to b(3,9,2) Select one: O…

A: We will find out the required value.

Q: 5. Suppose your universal set is U = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and we have the %3D %3D Find…

A: To determine the set.

Q: Let {C, : r € [0, 0)} be the family of indexed sets given by Cr {(x, y) E R : a? + y = r²} a)…

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Q: QUESTION 3 which of the following is the power set of the set S={ a, b, c}? {Ø,S} o{0,{a}, {b},…

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Q: QUESTION 18 Let U = {q, r, s, t, u, v, w. x, y, z} A = {q, s, u, w, y} B = (q, s, y, z} C = {v, w,…

A: A∩B∩C={q,s,u,w,y}∩{q,s,y,z}∩{v,w,x,y,z}={y}

Q: Given U = {a,b,c,d,e.f.g.h.ij) A = {b,d.f,hj} B = (e,f.g,h.ij} find the following sets. a. {f,hj} b.…

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Q: Given the following sets X= {a,b,c} Y= {a} Z= {a,d} In the universe U= {a,b,c,d,e}, what is (X’…

A: Sample Space (SS): The total number of possible outcomes of an event is called Sample Space and it…

Q: Given the following sets { a, b, e } {a} {a, d} in the universe U = { a, b, c, d, e }, what is…

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Q: QUESTION 8 Given the following sets: U = {a, e, i, o, u, q, r, s, t} A = {a, e, i, o, u} B = {r, a,…

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Q: Suppose {p, p,, P3} is an affinely independent set in Rn and q is an arbitrary point in Rn. Show…

A: Here, {p1,p2,p3} is an affinely independent set. So, {p1,p2,p3} are linearly independent.

Q: Consider the Venn diagram shown below. For each of (i)–(iv), copy the diagran and shade the region…

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Q: Let A and B be sets. Prove that A – B = AU B.

A: Let A and B be two sets. Now, A¯-B=A¯∩B¯ ⇒A¯-B=A∪B¯  by De Morgan's Law

Q: ---A 2 Let aj 1 and ag -10 The set {a1, az, ag} will span R unless h

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Q: Let A, B and C be any sets. Which of the following is equal to (A U C) n (B \ C)? Select one: a. (A…

A: Solution is given below:

Q: Let A, B and C be sets. Prove that  C ⊆ A ∩ B if and only if C ⊆ A and C ⊆ B

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Q: d) Let X, Y, Z be sets. Calculate |X UYU Z| if |X| = 50, |Y| = 90, |Z| = 71, |X n Y| = 8, |Xn Z| =…

A: Given that X, Y and Z be the three sets.

Q: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →…

A: The complete solutions is in given below

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”.