A subset S of IR" is convex if whenever it contains a and b it also contains the line segment joining them, that is, all points ta+ (I - t)b with O.:S t .::: 1. Show that if S and T are convex subsets of IR", then the set S + T of all sumsx+y,withxinSandyinTisalsoconvex

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: 3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in R+", then so is…

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Q: 11.0, Prove that the interior of the interin of a set is equal to the interies of that set

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Q: . Is it true that the null set is a subset of every other set? (Y/N)

A: If a set has no element then the set is called null set. Null set is also called empty set. It is…

Q: |x²| = p^ n

A: Given: X=pWe need to show that Xn=pn

Q: If #: $ a,b,c} which of these celations are a funchion? Emplain, cab) CS

A: Solution : Given :    A= {a, b, c}  Set of relations are      a)    { (a, b), (b, c), (c, c) }…

Q: 1. For each of the following sets, decide whether they are closed, bounded, compact (both) or…

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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: 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: 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: 4. (a) Write down four distinct elements of the set {2 €C:2- E = 2i}.

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: TOVE 4.55. Let A, B and C be sets. Prove that (A-B) (A-C)=A-(BUC).

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Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

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Q: 3) Prove using Venn diagram that An (BUC) = (An B) U (ANC) 4) Using equality of sets, prove that (A…

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Q: If D(L AOB) states the set of points located on the OA side containing point B and the OB side…

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Q: Let A and B be finite sets satisfying |A| = 6, |B| = 7 and |AN B| = 2. %3D Calculate the following:…

A: # we are entitled to solve three subparts at a time, please resubmit the other parts if you wish to…

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”.