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: 1. Given the points P(5, 3, - 4) and Q(7 - 1, - 3), find the following: a. the vector PO b. PQl

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Q: Let A = {3,4, 5, 6, 7}, B = {5, 6, 7, 8,9}, and C = {4, 7, 9}. Let U, the universal set, be…

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Q: Exercise 3.48. Let A,B,C,D be points such that AB = CD. Prove that {A, B} = {C,D}.

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Q: Let A, B and C be overlapping sets, verify following by using Venn diagram and membership table ((An…

A: Consider the provided question,

Q: 7) A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is 40…

A: Given: A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is…

Q: For the following Venn diagram, determine the set A -B. k h 2 a 4 10 5 11 A 15 d 7 14 1 12 B. 8. 13…

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Q: Ex 3.7.1 Construct the correspondences between the indicated sets. a) Z10 and Z2 × Zg b) Z15 and Z3…

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Q: Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one…

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Q: §7. (6 p) Let each set S1, S2 be formed by only one vector: S₁ = { Is S₁ LI, LD or neither? Is S2…

A: To determine if the given sets  S1​  and  S2​ , and their union, are linearly independent (LI),…

Q: Let Asfl,2,3} and The relations Ri=f(),(2,),(3,2) | find the following Ye lations

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Q: (5,,1) and i = (-8,6, –7), find the length and direction of u x v and v x u. '7 1 2' 2 Length of u x…

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Q: How many points need to be in a set in R° to guarantee that the set is affinely dependent? А. 11 В.…

A: According to the given information, it is required to tell the number of points in a set R9 to…

Q: Let u = = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that the angle between u −…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let A, B, and C be sets. (a) Find |(A U C) \ B|provided |A| = 50, |B| = 45, |C| = 40,|A N B| = 20,…

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Q: f. Connider the ret { KI, E, P, 21 , Q ,Q°, R*, R, C }, integers, P Q w the whee E i the set all…

A: Please check the answer in next step

Q: 1. Let u = (1,2,3) and v= (1, x, 0) and w= (0,1,0). a. Find ||u + w||. b. Find (u, u + w) + ||u||.…

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Q: Let = (1,2). - a. Explain graphically the set S = {(x, y) : (x − 3, y − 1) · ʊ = 0}. b. Draw the the…

A: v→=1,  2 S=(x, y) : x-3, y-1·v→=0

Q: Suppose v = (2, 5, 4), |w| = 3 and the angle between v and w is 30◦ (a) Find v · w (b) Find compvw…

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Q: Given the following​ sets, find the set left parenthesis Upper A prime intersect Upper B right…

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Q: §7. (6 p) Let each set S1, S2 be formed by only one vector: S₁ = { Is S₁ LI, LD or neither? Is S₂…

A: In linear algebra, a set of vectors is said to be linearly independent if no vector in the set can…

Q: 3. Find the value(s) of a for which ở = (-1, 2a – 1,3) and w = (2,2a + 3,–6) are parallel.

A: Two vectors  are parallel  is their cross product  is zero. So calculate  cross product  in the…

Q: QUESTION 14 For the following Venn diagram, determine the set c - A: C-A k 10 C. h 2 a 4 11 9. A 15…

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Q: A free vector is Select one: O a. a directed line. O b. a directed line-segment in 3- space. c.…

A: A vector whose point of application is not fixed but magnitude and direction is, is called free…

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: If vector r = ❬5, 11❭ and s = ❬9, –8❭ then which is r – s?  a r – s = ❬–14, 3❭  b r – s = ❬–4, 19❭…

A: r=5,11 and s=9,-8

Q: 14. Let vy 3 and b= Which of the following statements is true? A. b is a linear combination of vy…

A: Vectors.

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”.