B is between A and C, D is between A and E.

2. Let A = {a, b, c, d, e}, B={a, b, c, d, e, f, g, h} and C = {2, 4} (a) 4 U B= (b) 4 intersection B= (c) A - B= (d) B - A= (e) A x C =
Prove that if a,b,c,d e Z and aſc, b|c, and the GCD of a and b is d then ab|cd 8 Format BI U
4[10 pts]. Let f(z) = u (r,0) + iv(r,0) be analytic in a domain D c C which does not contain the origin. Then do the following ones: (a) Show that rurr(r, θ) + rur(r, θ) + u69(r, θ) 0 for all re® E D. (b) Show that (a) is equivalent to the condition that u is harmonic in D (c) Show that the function (in|e )2-[Arg( a(z) z)]2,-π < Arg(z) < π,
4[10 pts]. Let f(z) = u (r,0)...
me that E(UIX)=0(that a (a) What is E(U) and E(UX)? (b) What is the correlation between X and U? (c) Show that E(Y|X) =a+bX, and that E(Y) = a+bE(X). Let Y a + bX + U, where X and U are random variables and a and b are constants. Assume that E(UX)0 (that is E(UX ) for all possible x
PULUIJ UIT IS ALTUUS. b.. What is the difference between a trapped value and new to the world value? c. . What comprises an online business model? d. The term Context in an E-business customer interface can be viewed as visuality of Explain e. Identify and explain three desirable properties of digital money (3 Marks Each)
Let 0 < a <b<e<d for a, b, c, d E R. Consider the set S={(u, ujo < u < 1, 0<u<1) and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the r-y plane for the case ad - be>0. (a) Sketch D in the r-y plane for the case ad - be < 0. (c) Calculate the area of D. Show all working.
Let L = {w! w can be written as cd#e#c with c, d, e e {a,b}* }. Show that is not regular.
Let X = {a,b,c,d,e) and T = {X, Ø, {a}, {c,d}, {a,c,d}, {b,c,d,e }} and {A= {b,c,d {interior(A)= {cd a {interior(A)= {a,c,eb {interior(A)= {d.c {interior(A)= {a,c,d .d
36 5° D 75° A Caterpillar Ultra High Demolition machine is shown. The distances between points A and B is 12 m, points B and C is 2.8 m, C and D is 8 m, and D and E is 2.5 m. Determine the position vectors r AB r BC r CD , and r DE where r AB is the position vector from point A to point B, and so on. Add these vectors to determine the position vector...
(b)
Let D C C be a regular domain, f : D → D' C C be a complex-valued function and f(z) = u(x,y) + iv(x,y). (a) Show that if/(z) is differentiable on D implies the Cauchy-Riemann equation, i.e., au dyJu on D. (b) Assume that D- f(D).e. fis a conformal mapping from domain D onto domain D. Le x' =a(x,y), y = r(x,y). Show that if φ(x,y) is harmonic on D. ie..知+Oy-0, then is also harmonic on domain D....