Choose the correct option. Let S be the set of points whose abscissas and ordinates are natural numbers . Let P∈S such that the sum of the distance of P from (8,0) and (0,12) is minimum among all elements in S . Then the number of such points P in S is- (a)1        (b)3    (c)5    (d)11.

Q: 12] and a3 = -20 4 -------- Let a₁ = h 5 2 The set {a1, a2, a3} will span R³ unless h = 0

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Q: 1 Determine whether or not the three given points le on a ne A (1,1,2), B(-1,-9, 3), C (3,2,1) 2.…

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Q: Let P1, P2, P3, .. , P78 be some coplanar points with k lines on the same plane. If exactly two line…

A: Given,  P1, P2,P3,...,P78 be some coplanar points with k lines on the same plane. If exactly…

Q: Find the intersection of the sets. {s, e, t}∩{t, e, s}

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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: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: CustomerT batslgmos dmn svig ai a W Y Z. done 10 2 8 on 6. 4 12 8. 14 10 8 2 D 4 14 10 8. Тaxi

A: Hungarian  Method-2 :-

Q: 2.5.22. Let A, B,C be three sets. Prove that if A \ B C C, then A \C C B.

A: Given: Let A,B,C be the three sets. A-B contained in C

Q: b. Explain that is {(1, 3), (2, 2), (3, 1)} a permutation function on set A = {1, 2, 3}? if it is a…

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Q: a) Show that the set S = {(1, 2, 3), (0, 1, 2), (– 2, 0, 1)} spans R³. b) Determine whether the set…

A: See the attachment.

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Use graph to find  set. [1, 3) ∩ (0, 4)

A: Given set is  [1, 3) ∩ (0, 4) The graph of the given set is as shown

Q: A How many paths are there from A to C?

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Q: et A, B, C and D be sets. Prove that (AnB)u(CnD)=(AUC) n(BUC) n(AUD)n(BUD)

A: The set A∪B contains all the elements that are present either in set A or in set B. The set A∩B…

Q: Which of the following is NOT a subset of 2 {a,b} x {a,b} ☐ ({a}, a) (a, {a}) ({a,b}, {a,b}) ☐ ({a},…

A: In set theory, a subset relationship denotes that every element of one set is also an element of…

Q: Find the indicated sets. (a) P({1,2} × {3}). (b) P({1,2}) × P({3}). (c) {X e P({1,2,3}) : 2 EX}.

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Q: For all sets A, B, and C, prove that (AUB) - (CA) = AU (B-C) Please indicate the reason for each of…

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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 that you have two sets, and you know that both sets are convex. Proven that the intersection…

A: convex set is a set of points such that, given any two points x,y in that set, the straight line…

Q: Show by example that the union of two convex sets need not to be convex.

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Q: Let X be a set. Show that P(X)÷ X.

A: Solution:Let X ba a set.To Prove: P(X)≠X

Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let A and B be sets. The symmetric difference of A and B, denoted A∆B, is the set A∆B = (A −B) ∪(B…

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Q: For the poset, R = ( { 1, 2, 3, 5, 10, 15, 20, 25, 30, 35, 50, 70 }, | ):   Draw the Hasse digrams…

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Q: A set L cR is convex if:

A: In this question, we have to find the correct option for the convex set L⊂Rn  here we use the direct…

Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

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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: 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: 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.

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”.