(14) Show that if [(a1,b)- [(a2, b2) and [c,d) (c2, d2)] and bidi(aidi -b)>0 then b2d2(azd2 - b2c...
13) We continue to consider as in the previous problem, and denote the class of (a, b) by [(a, b)] for a є Z and b є Z、(0). Show that if [(al, bi )]-[(a2, b)] and [ci, di)-[(C2'の] OW d2, 02) an en a1C1, 01d1 the proposition which allows us to know that multiplication on Q is well-defined.) 13) We continue to consider as in the previous problem, and denote the class of (a, b) by [(a, b)] for a...
(a) Let P(B1∩B2)>0, and A1∪A2⊂B1∩B2. Then show that P(A1|B1).P(A2|B2)=P(A1|B2).P(A2|B1). (b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in this case, A and B1∪B2 are independent if and only if A and B1∩B2 are independent. (c) Given P(A) = 0.42,P(B) = 0.25, and P(A∩B) = 0.17, find (i)P(A∪B) ; (ii)P(A∩Bc) ; (iii)P(Ac∩Bc) ; (iv)P(Ac|Bc).
e) Use the triangle inequality to prove that (ac + bd)2 (a2 + b2)(c2 + d2) for all a, b, c, d e R. Total: [20 marks] e) Use the triangle inequality to prove that (ac + bd)2 (a2 + b2)(c2 + d2) for all a, b, c, d e R. Total: [20 marks]
Imagine that the hypothetical elements. A B C and D form the ions A2+, B2, C2, and Dar. The following reactions show the interactions that do or do NOT occur. Use this information to order the species in a reduction half reaction table. D2+ + C → C2+ + D Easiest to Hardest to Reduce Oxidize D2+ + B - No reaction C2+ + A - A2+ + C Hardest to Reduce Easiest to Oxidize st Lab Questions: To receive...
Substances A2, B2, and C2 can all act as oxidizing agents. In solution, A2 is green, B2 is yellow, and C2 is red. In the reactions in which they participate, they are reduced to A-, B-, and C ions, all of which are colorless. When a solution of B2 is mixed with one containing C ions, the color changes from yellow to red. a. Which species is oxidized? b. Which is reduced? When a solution of B2 is mixed with...
Given the following equations: (i) B2+ + C --> B + C2+ doesn't go (ii) D+ B2+ --> D2+ + B (iii) 2 A3+ + 3D --> 2 A+ 3 D2+ doesn't go Arrange the elements A, B, C, and D from the strongest to weakest reducing agent. goes
GAME 3 Player B B1 B2 Player A A1 7,3 5, 10 A2 3,8 9,6 In Game 3 above, if the players move sequentially with Player B choosing first, the Nash equilibrium will be a) Player A choosing A2 and Player B choosing B1 b) Player A choosing A2 and Player B choosing B2 c) Player A choosing A1 and Player B choosing B2 d) Player A choosing A1 and Player B choosing B1
2. (a) Let P(Bin B2) > 0, and AUA, CBin B2. Then show that P(A/B).P (A2|B2) = P(A|B2).P (A2|Bi). (b) Let A and Bbe independent; similarly, let A and B, be independent. Show that in this case, A and B U B2 are independent if and only if A and Bin B2 are independent (c) Given P(A) = 0.42, P(B) = 0.25, and P(An B) = 0.17, find (i) P (AUB); (ii) P(An B°); (iii) P(A n B); (iv) P(...
C4v E 2C4 C2 2sigmav 2sigmad A1 1 1 1 1 1 z A2 1 1 1 -1 -1 Rz B1 1 -1 1 1 -1 B2 1 -1 1 -1 1 E 2 0 -2 0 0 (x,y) (Rx, Ry) The C4v character table is given above. Prove that the following combinations of irreps are orthogonal. a) B2 E b) A2 B1 c) A1 B2
Mark True/False for functional dependencies of the following table R(A, B, C, D, E), where we assume that it is the intent of the designer that exactly this set of rows should list in the table. A B C D E a1 b1 c1 d1 e1 a2 b2 c2 d2 e2 a1 b1 c1 d1 e2 a2 b2 c3 d4 e2 (a) A --> B (b) B --> A (c) C--> A (d) D --> A (e) CD --> B