4 [8 pts. Consider sets A, B, and X. Recall 2 is the powerset of set...
Question 8 4 pts A relation Rfrom a set A to a set Bis a subset of а. А х А b. Вх В с. Ах В d. B x A d. Question 9 4 pts A relation Ron a set A is an equivalence relation if either of the following is true: (a) Ris reflexive on A (b) Ris symmetric on A (c) Ris transitive on A. True False
Consider two data sets. Set A: n = 5; x = 4 Set B: n = 50; x = 4 (a) Suppose the number 14 is included as an additional data value in Set A. Compute x for the new data set. Hint: x = nx. To compute x for the new data set, add 14 to x of the original data set and divide by 6. (Round your answer to two decimal places.) (b) Suppose the number 14 is...
Question 8, please. 2. Prove: (a) the set of even numbers is countable. (b i=1 3. The binary relation on pair integers - given by (a,b) - (c,d) iff a.d=cbis an equivalence relation. 4. Given a graph G = (V, E) and two vertices s,t EV, give the algorithm from class to determine a path from s to t in G if it exists. 5. (a) Draw a DFA for the language: ( w w has 010 as a substring)....
(5 pts) Give an example of a relation on a set that is a) both symmetric and antisymmetric. b) neither symmetric nor antisymmetric. (3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n =1 An = {0} (b) Um_1 An = [0, 1] (c) n =1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category...
Name that Parametrization 4. (a) Consider these two sets of parametric cquations: x(1)-1 y(t) = sin t 0<t<oo x (t) sin t y(t) = t 0<t<00 What is the difference between their associated curves? (b) Given any set of equations of the form What does the graph of the set of equations y(r) = 1 x(!) = f (1) 0<t<oo look like? Use a calculator to check that f(x) = x5-3x3 + 5x + 2 is one-to-one. 5, (a) (b)...
Question 8 (Chapters 6-7) 12+2+2+3+2+4+4-19 marks] Let 0メS C Rn and fix E S. For a E R consider the following optimization problem: (Pa) min a r, and define the set K(S,x*) := {a E Rn : x. is a solution of (PJ) (a) Prove that K(S,'). Hint: Check 0 (b) Prove that K(S, r*) is a cone. (c) Prove that K(S,) is convex d) Let S C S2 and fix eS. Prove that K(S2, ) cK(S, (e) Ifx. E...
QUESTION 20 Match the set operation with its definition. SAB 8 (x|x 6A and x6 B) b.[xIX EA or X EB) - BAUB BA CXIX EX and x A) CHA-B d. (X|XE A and B) QUESTION 21 Given A=(u.w,x,y), B = {s,t,u,v.w} find the following sets. AUB - BANB SA atr.z) b. (X.) (r,s.t.v,x,y,z) d. (s.tv] - (AUB) - B(ANB) - AUB ABC -A-B AB-A (uw) 4. (5.,..W.X.V) 9.(r.5.6.v.z) h.(r.x.v.) QUESTION 22 Given the sets A=(5,7) and B = {x,y,z)...
4. Consider the set S = {(x, y) | x ∈ [0, 1], x2 ≤ y ≤ x}. Prove that S is a Jordan region and integrate the function 2x 2 + 3y 2 on S.
Question 2. Recall that a monoid is a set M together with a binary op- eration (r,y) →エ. y from M × M to M, and a unit element e E/, such that: . the operation is associative: for all x, y, z E M we have (z-y): z = the unit element satisfies the left identity axiom: for all r E M we have the unit element satisfies the right identity axiom: for all a EM we Let K...
please lease solve all questions. 2. Consider the following two variables X and Y: 4 a. (2 pts) Find the mean of X, and mean of Y b. (2 pts) Find the standard deviation of X, and standard deviation of Y C. (3 pts) Find the covariance between X and Y d. (2 pts) Find correlation coefficient between X and Y and comment on your answer. 3. The following table shows a random sample of 100 hikers and the areas...