EÇIR is connected. E is one of the following sets 6 , IR, [a, b] ,...
Problem 1 (5 pts): What can you say about the relation between sets A and B if we know that (a) AUB= AY (b) A - B = A? (c) AB =A? ASB That is when ACBB CA, or AB=.
8. Suppose that A and B are both connected sets in a metric space X, and that the inter- section An B is not empty. Show that the union AUB is a connected set. (Consider non-empty open sets U, V in AUB, whose union equals AUB. Show that U and V both contain An B, so U and V cannot be disjoint.)
Which one of the following compounds is consistent with the following IR spectrum? کے 3000 4000 8 2000 A) I B) II C) III D) IV E V Select one: O a. V O b. IV OOO d. page Finish attempt ... igation mpt.
6. The sets A = {n E N: n2 〈 25) and B denotes the set of natural numbers {n2, n E N and n 〈 5} are equal. Here N
6) If E is any countable subset of real numbers prove that A*(E) = A*(E) = 0. 7) Show that the set of all real numbers IR is measurable with >(IR) = . 8) Prove that If f : [a, b] IR is continuous [a; b]then it is measurable [a, b]. 9) Give an example of a function f : [O, 1] IR which is measurable on [O, 1] but not continuos on [O, 1]. 10) Find the Lebesgue integral...
6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by deleting that edge (V(G) V(G) and E(G) E(G) \<ej) is not connected. Prove that if G1 and G2 are connected simple graphs which are isomorphic and if G1 has a cut edge, then G2 also has a cut edge....
. 6. (10 points) Given the universal set U = {a, b, c, d, e, i, o, u, x, y, z}, and three sets A = {a, b, c, d, e}, B = {a, e, i, o, u}, C = {0, u, x, y, z}. Find the following sets (a) A UB (b) COB'
6 Let A and B be two sets of real numbers and write Clr E A,yE B a) Find a relation among supA, supB and supC b) Find a relation among infA, infB and infC
The IR/spectrum shows the value, 1st photo shows the instructions. Attached are 2 sets of spectra. Each set is worth 25 points. Not all sets have a Mass Spectrum, but do have information that was obtained from MS and some sets do not have a "C-NMR and don't really need one. Look at each spectrum individually and clearly list and comment on the structural Characteristics you can determine from that spectrum. (Chemical shifts, splitting patterns, coupling constants, fragmentation patterns, absorption...
1.) Prove the following theorem Theorem 3.4.6. A set E C R is connected if and only if, for all nonempty disjoint sets A and B satisfying E AU B, there always erists a convergent sequence (xn) → x with (en) contained in one of A or B, and x an element of the other. (2) (10 points) Are the following claims true or false? You must use the ε-δ definition to justify your answers. x-+4 r2 16 (Here [[x]-greatest...