21. Let A and B be two non-empty bounded sets of positive numbers and let C = {xy : x e A and y e B}. Show that C is bounded and that Sup C: = sup A. sup B,

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: What is the global minimum of the function, x² 5 f(x) 3 + 2 on the interval [-2, 2] ? a) 2 b) 23 3…

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Q: X, Y and Z be subsets of the set . Verify the following propert XU(YUZ) = (XUY)UZ, XN(YnZ) = (XnY)…

A: X, Y, Z be subset of a universal set Ω to verify…

Q: Consider the set V = {(x, y) = R² : x+y=1}. on this set defined in the following way: (x2, y2) = (x₁…

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Q: Dijec not need to prove you function is a bijection): (a) N and Z (b) Rand (1, ∞) (c) (0, 2) and (3,…

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Q: (a) Determine whether or not it is convex or concave. A = {(x, y) = R²|yx4, and -2≤ x ≤ 2} B = {(x,…

A: Necessary Sufficient Nature f'x0=0 f'x0=f''x0=f'''x0=..=fn-1x0=0  fnx0>0 n even Convex f'x0=0…

Q: 5. Are the following true or false, and prove your answers: (a) If A is compact and B is bounded,…

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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: . 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: Let X = {1, (b) xm} and Y = {y₁, Yn} be finite sets. Determine the number of one to one functions…

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Q: Let A, B C X be subsets and f : X → Y a function. Show that ƒ(AÑ B) ≤ f(A)Ñ ƒ(B)

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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: 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: 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…

Q: 2- Find the set of lower bounds and the set of upper bounds of the following sets in Q, if it…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose that A and B are sets and f : A –→ B is a function. Fix subsets X,Y C A. Prove that Imf(X) –…

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Q: 3.) Which statement comparing the test scores of 1st Period and 2nd Period is FALSE? Test Scores 1st…

A: From the given box plots:   Range of 1st Period=98-60=38 Range of 2nd Period=95-70=25   Therefore,…

Q: 6.3. Let (A, <A) and (B,<B) be two partially ordered sets. One can define on the cartesian product A…

A: Given: A, ⩽A and B, ⩽B are partially ordered sets.  A Cartesian product A x B is defined with…