22. Let A be a bounded subset of R and let sup A = B. Which of the following is/are not an attribute of B? I: VE > 0,3 x € A 3 B- e

Q: Which of the following sets is a linearly independent set? a. (1,2),(5,10) b. (1,2),(5,8) c.…

A: Linearly independent and dependent set

Q: Show that the set S= {(1, 2, 1), (3, 1, 5), (3, -4,7)} u de nendent where. SCV (B). is linearl

A: We need to find scalars c1, c2, and c3, not all zero, such that   c1(1, 2, 1) + c2(3, 1, 5) + c3(3,…

Q: Vhich of the following sets is a null set ? I. X {x | x= 9, 2x = 4 } II. Y {x | x= 2x, x #0 } III.…

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Q: (a) An (B − A) = Ø.

A: Given data:- The given equation,  A∩(B-A)=φ

Q: Ex: Let X₂ [1,2,3,4,5]. I. [0,X, [1], 82.3, 81.23], Y. [3,4,5,6,73 andl T₁: [0, X, [4], [4,633 if A:…

A:

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,…

A:

Q: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: Which of the following sets is a function? * {(a, a)b,b)\a,c)} {(a,b){b,cXc,a} Option 2 О Оption 4…

A: We have to identify which of the following set is a function.

Q: Let a1 = [-2  h], and a2 = [10  -20] The set {a1,a2} will span R3 unless h

A:

Q: 6. Suppose that inf A > inf B. a. Show that there exists a € B such that a is a lower bound of A. b.…

A: 6a) Given: Two sets A and B such that infA>infB, To Prove: there exists an element a∈B which is a…

Q: 11. Let A(3, 4, 5) and B=(4,5,6) and let S be the "divides" relation. That is, for all (x, y) e Ax…

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Q: Which of the following sets spans R³? {(0,1,-1)} None of these O {(0,1,-1).(0,0,0)} O…

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Q: {(r.0):3<rs4 and so<- Neatly sketch the set of points

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Q: Let a, b € N. Choose all correct statements. O gcd(-a, b) = gcd(a, -b) O ged(2a – b, a + b) =…

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Q: . Sketch the graph of the set defined by A x B where A is the closed interval [-2, 4] and B = {1, 3,…

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Q: Use any method you choose to shc are sets.

A:

Q: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

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Q: F and Hare sets of real numbers defined as follows. F = {ww≤ 4} H = {w|w>5} Write FUH and FnH using…

A: We can find the union and intersection of sets in the below steps.

Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: 9. S= {(6,2, 1), (-1,3,2)} is: %3D linearly independent set of R. b. a linearly dependent set of R3.…

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Q: 5. Let D = {1, 2, 3, 4, 5}, C = {a, b, c, d}, and g = {(1,a), (2,c), (3,d), (4,c)}. Determine…

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Q: Determine whether the given set is linearly independent.

A: We will check that given set is linearly independent or not using definition of linear independency.…

Q: Suppose A and B are nonvoid, bounded, disjoint subsets of R. Mark all of the properties that must be…

A: A and B are nonempty bounded disjoint subset of ℝ

Q: Q3. Suppose A = {1,2,3,4}. Which of the following sets is the relation R = {(a,b)|a+b is odd }? A. R…

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Q: II. Let Q-set of all real numbers, A-index set. Identify the generalized union and intersection of…

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Q: Give an example of four sets A, B, C and D such that (AUC) x (BUD) ≤ (A x B) U (C x D).

A: The set A is a subset of B if every element of A is in B

Q: . Given the relation R1 from X = {1,2,3,4} to Y = {a,b,c} and R2 from Y = {a,b,c} and Z = {6,7,8}…

A: Here given  Relation R1 from X=1, 2, 3, 4 to Y=a, b, c is defined as R1=1, a, 2, a, 2, b, 3, c, 4,…

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: Let v = (5, 1, 2) and w = (4, –3, 6). Find each of the following: v+ w, v– 3w, || v||, || v – w ||

A: Solution: The objective is to find the required values

Q: denumerable. Apply the definition and prove that the set A = {₁, {} ... } is

A: An infinite set is denumerable if it is equivalent to the set of natural numbers I.e there is a…

Q: Which of the following sets are convex and which are not? 2 a. {(x₁, x₂) x² + x²₂² ≥ 3}. b. {(x₁,…

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Q: Let A = {1,2,3, 4} and B = {a, b, c, d, e}. How many different relations are there from A to B. Why?

A: Given A=1,2,3,4B=a,b,c,d,e

Q: Let a < b. Find the crossing point n0 at which c1na = c2nb, for any c1, c2.

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Q: Show that the interval [0,1] is a closed set in R

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Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: T T T T F 18. Let A and B be sets then A + B if, and only if A ¢ B and B ¢ A. For sets A, B, and C,…

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Q: The set {[1 2 0 1, [2 0 4 1, [O 4 5 ]}spans R3 صواب İhi

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Q: I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 8. For any sets A, B,…

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Q: Let a = (5,-2, 9). Find ||10||

A: