If Si and S2 are convex sets, is their union S1 U S2 a convex set. Explain your answer.

Q: Which of the following are difference sets?

A: Introduction: A (v, k, λ) difference set is a k-element subset D of V = Z (mod v) in which any…

Q: Given, A={0,1}, B=null set C= {2,3} Find A xB, A X C, A u B, A\B, A\c, AX C, B intersection C and…

A: our objective is to find the solution.

Q: Come up with an open interval A and closed interval B such that A∪B = (1, 10] and A ∩ B = [4, 5).

A: our aim to find the examples satisfying A - open interval  B- closed interval  such that A∪B = (1,…

Q: If R is the universal set, find: 1. Q ∩ R 2. Z ∩ I 3. N ∩ I

A: Since R is universal set.

Q: Find: geometric mean for the y set

A: Our aim is to find the geometric mean for the y set.

Q: , B, and C which satis

A: Given as, A= {1, |B|, |C|} B= {2,| A|, |C|} C= {1, 2, |A|, |B|}

Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: In this question we prove that certain sets are not convex. For each of the following sets, give the…

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Q: Come up with an open interval A and closed interval B such that A∪B = (0, 4) and A ∩ B = [1, 2].

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Q: Which of the following are difference sets? (iii) {3, 6, 7, 12, 14} in Z21.

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Q: Suppose A and B are sets such that |A| = 2 and |B| = 3. What is |P(A x B)|?

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Q: Let A, B, and C be sets. Is the following equality true or false? A x (BUC) = (A × B) U (A × C')

A: Sets, distributive law

Q: (а) An B 3 o (Ъ) в СА (с) АДВ — AU B.

A: The detailed solution is as follows below:

Q: Below are true statements on the intersection of convex and nonconvex sets: Select one or more: O a.…

A: Result: We know that any collection of convex sets (finite, countable or uncountable), their…

Q: What is the size of the union of the sets A and B, if |A|=|B|=12 and |ATT B|=10?

A: The sets A and B,A=B=12 and A∩B=10

Q: State whether each of the following set is finite or infinite:(i) The set of lines which are…

A: :Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Are the sets A_4 and A_5 compact sets? Why yes, why not? Ay = (,2] A- [1, 2] u [ 3, +]

A: See the attachment

Q: Consider whether the following statements are true or false: a. The intersection of any two convex…

A: To state true or false

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

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Q: Let A and B be sets. Then B (B – A) is equal to the above A N B

A: The Venn diagram for 2 sets can be drawn as follows.

Q: R, S and T are closed sets implies RnSnT is closed.

A: given

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: For any two sets A and B, if m* (A) = 0, then m* (AUB) = m* (B). In particular, if BCA, then m* (B)…

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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: What can you say about the sets A and B if we know that a) A ∪ B = A? b) A ∩ B = A? c) A − B = A? d)…

A: (Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Does the set S = {(1,2, 3), (0, 1, 2), (-2,0, 1)}span R³? %3D O Yes O No

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Q: a) DeMorgan's laws tell us that for sets A and B, the expression (Aº n Bº)° simplifies to

A: For two sets A and B the De Morgan's Law states that A∩BC=AC∪BC.

Q: Consider sets A={1,3,5} and B = {2,4,6}. find A ∩  B

A: We apply the property of intersection

Q: Which set represents the same relation as the gra 4 2- 6-5-4-3-2-1. 1 2 3 4 56 2. -3. 寸 LO CO ....…

A: Given graph is

Q: Which of the following are difference sets? (ii) {0, 1, 3, 5} in Z13,

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Q: Is this statement true or false.  Justify your answer. (Discrete Math)   For all sets A, B, and C,…

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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: the diagram for the intersection of sets A and B.

A: Basic concepts intersection of two sets- Let A and B are any two sets, then the intersection of sets…

Q: Without graphing, determine which of the followingdata sets are exactly linear, approximately…

A: You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y…

Q: determine which of the following sets are equivalent to the set (x,y,z) a. (w,x,y,z) b. (1,5,17)…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: Refer to the following Venn diagram, and list the points that belong to each set. (Enter your U A •y…

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Q: Is this set finite or infinite? {x € R|1 < x < 2}

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Q: If S1 and S2 are convex sets, prove that their intersection S1 N S2 is also a convex set.

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Q: Are the following pair of sets equal? Justify your answer? A = { x:x is a letter in the word FOLLOW}…

A: Set: A set is a well-defined collection of distinct objects. Equality of Sets: If two sets A and B…

Q: Let S1, S2, S3 be convex sets. Is their intersection nS, necessarily a convex set If 'yes' show, if…

A: A set S is convex if the line segment joining any two points lies in S That is  A set S is convex if…

Q: Show the following set is convex. x≤10 [(1+(x-10)-²)¹ x>10 Determine a-cut sets of the above set for…

A: To show that the given set is convex: μAx=0                               x≤101+x-10-2-1  x&gt;10…

Q: Show that the feasible set X = {r: g1(x) < 0,..., gr(x) <0} is a convex set, if all the functions 9;…

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Q: If X and Y are two sets, then X∩(Y∩X)c equals a. Ø b. Y c. X d. X∩Yc

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Q: Is the set {A, T,1} complete? Support your answer.

A: For a set of operators to be functionally complete, the set can be used to express all possible…

Q: Let A and B be sets. Then B - (B – A) AN B is equal to the above

A: Let A and B be sets  Let x∈B-B-A ⇔x∈B and x∉B-A ⇔x∈B∧x∉B∨x∈A⇔x∈B∧x∉B∨x∈B∧x∈A⇔x∈B∧x∈A⇔x∈A∩B ( since…

Q: If the class boundaries are 16.45 20.55, then the class interval is ......

A: Class intervals is given by 16.50 - 20.50 Then we get class boundary as  (16.50-0.05)  -…

Q: The Cartesian product of finite and nonempty sets can be illustrated by the intersections of a…

A: Given:  a=nA and b=nB To find: Explain why the number of intersection points in the crossing line…

Q: Decide, among the following sets are subsets of one and another: A={x:x ER and x satisfy : x - 4x +3…

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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”.