a) Show that the set S = {(1, 2, 3), (0, 1, 2), (– 2, 0, 1)} spans R³. b) Determine whether the set S = {1, x², x² + 2} spans P2. %3D

Q: Use the Venn diagram shown to answer the question below. U A B II III V IV VI VII VIII Which regions…

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Q: 2. Let A = {r|x is older than 25}, B = {y|y_is older than 50}, C = {z |z is between 20 and 30}. Draw…

A: The question is related to sets. The solution is explained below.

Q: Find the number of elements in sets A, B, and C using the given information. AnC-Ø,n (An B) = 6, n(C…

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Q: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

Q: Consider the sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is not…

A: Consider the sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is not…

Q: Find the dimension of the set S= {(2, 4), (4, 8)}?

A: The dimension of the set S can be find out by finding the linearly independent vectors in it.…

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: Let X={a,b,c,d), f = ((a,b),(b,a),(c,c),(d,d)}CX×X, and g= ((a,d),(b,a),(c,b),(d,c)}CX×X. Find gof.…

A: Use the definition of composition of functions to solve this problem as in next step.

Q: 1. Find the sets of interior points and boundary points of each set and classify the set as open,…

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Q: Consider A = (x, y,z) and B = (w,x, y). If U = A U B, which set is equal to (B\A)'? Note: B\A = B-…

A: The union of set A and B is denoted by A∪B has elements both inset A and B The complement of A has…

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: Let U = {x | x is a letter in the word %3D GUADALARAJA}, where this is the universe set. Also, let M…

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Q: Describe the following sets by roster method: Example (i) {x : x + 5x + 6 = 0, x e N} (iii) {x : 4x…

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Q: 4. Find the following sets, which are subsets of R2. (a) U {a} x [0,1], (b) N {a} × [0,1], aeR aER…

A: Note: According to Bartleby guidelines; for more than three questions asked, only the first three…

Q: Consider the set S = {zeC:0< Re(z) < 2 & 0<Im(z) < 3} What is its interior? {zeC:0<Re(z) < 2 & 0<…

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Q: Exercise 1. Prove that for sets A, B,C we have C \(AUB) = (C\ A) N (C \ B).

A: We have to show that for sets A, B, C   C ∖(A∪B)=(C∖A)∩(C∖B).

Q: (10) Show that the set A = {a € Q : a² < 2 or a < 0} is a %3D cut.

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Q: determine whether set s={(2,1),(-1,2)} spans R^2

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Q: Use the listing method to express the set S = ((1,3] x {2,4}) n z².

A: Given, S=(1,3]×{2,4}∩ℤ2 We have to express it in the Listing method, As we know, ℤ2=(a,b) where…

Q: Let A, = (1, 2), A2 = (x, y, z), As = {a, b}. Find the following Cartesian %3D products. 1. AxA,.…

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Q: Find the union of the sets. {e, m, p, t, y}∪∅

A: we have to find the union of the sets. e,m,p,t,y∪∅

Q: 4 10 11 •12

A: To find the elements of the sets x,y and z from the given venn daigram.

Q: Select the law that establishes that the two sets below are equal: Gn (GU Z) = G OAbsorption Law O…

A: Sets identities

Q: By inspection, determine if each of the sets is linea (a) S= {(1, -2), (2, 3), (-2, 4)} O linearly…

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Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: Find sets A, B and C such that A ∩ B,    B ∩ C and A ∩ C are non-emptysets and A ∩ B ∩ C = φ.

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Q: Let A, and Az be two subsets of R. Show that m. (A, x A2) S m*(A,) m*(A2).

A: To prove: m*(A1 * A2) ≤ m*(A1) m*(A2)

Q: Show whether the sets are connected or not. 1. {z € C | 1< ]z| < 2} 2. D(0, 1) U D(2i, }),

A: 1. Given: D⊂E⊂A then D=E    To Find: To whether the sets are connected.   Where z=x+iy           z…

Q: Which of the sets that follow are spanning sets forR3? Justify your answers. {(1, 0, 0)T , (0, 1,…

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Q: 7. Shade in the region(s) that represent the set AU(B'nC) A

A: Answer and explanation is given below...

Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: Use Venn Diagrams to find A \ B and B \ A where A = {1,2,3} and B = {2,3,4}

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Q: Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C Ax (BUC) = (A x B) U (A x C),…

A: SOLUTION-

Q: Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly…

A: We have to check whether given set of vectors linearly independent or linearly dependent by known…

Q: Find the intersection of the sets. {w, y, z}∩∅

A: Given, w,y,z∩∅we have to find intersection of the sets.

Q: Find c such that (5,−9)(6,3), and (c,8) lie on a line. c=

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Q: (ii) Find a connected subset of R² which is not convex.

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: find the complement of set B, given that U= {x ∈ z/ - 7 < x < 7}     A= {x ∈ z+ /2 < x < 6}     B=…

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Q: The vectors {x+1,x2+x+1,x2+2x+1} form a spanning set for P3

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Q: Let S = {(1,1), (1, 2), (2, 1), (3, 2), (3,3)}. Consider the polytope conv(S). Write this set as {r…

A: The given set is S=1,1,1,2,2,1,3,2,3,3. We know that the polytope:…

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: Suppose we assign every element of Z xZ (think coordinate plane) one of three colors: cyan, magenta,…

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

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Q: Write out the subsets A, B,C defined below by listing their elements between braces. A = {x € S : x²…

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Q: Consider the two sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is…

A: Given :               The sets A = a,e,i,o,u   and B = c,m,n,r,s,v,w,x,z

Q: Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)are in A × B, find…

A: In AxB the first element will be from A and the second element will be from B So, x,y,z are in A And…

Q: 3A, B E {sets} such that A CBAA= B.

A: To check whether the given statement true or false: ∃A,B∈sets such that A⊆B∧A=B

Q: 2 Find values for a, b, and c such that is an orthogonal set.

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Q: Consider the two image subsets. S, and S, shown in the Following figure. For V {1}, determine…

A: Given:

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”.