If G={e, a, b, c, ...}. The set Inn (G)={phi e, phi a,
phi b, phi...
If G={e, a, b, c, ...}. The set Inn (G)={phi e, phi a,
phi b, phi c, ...} is called the set of inner automorphisms. Prove
that Inn(G) is a group under the operation of function
compositions.
Consider the relation R= {A, B, C, D, E, F, G, H} and the set of
functional dependencies: FD= {{B}—> {A}, {G}—> {D, H}, {C,
H}—> {E}, {B, D}—> {F}, {D}—>{C}, {C}—> {G}} 1) Draw FD
using the diagrammatic notation. 2) What are all candidate keys for
R? 3) If delete {C}—>{G} and change {C, H}—> {E} to {C,
H}—> {E, G}, what are all candidate keys for R
Seven people (A,B,C,D,E, F, and G) are seated in a row. Suppose
A,B, and
C are freshmen, D and E are sophomores and F and G are juniors. How
many
arrangements are possible if:
(a) D and F must sit together?
(b) A and C must not sit together?
(c) All freshmen must sit together?
(d) All freshmen must sit together, all sophomores must sit
together, and all
juniors must sit together?
(e) Exactly two people sit between A and...
1) Provide a set of payoffs in this format
a, b | c, d
e, f | g, i
for a 2x2 game that illustrated the problem of free access to
guns.
2) Provide a set of payoffs in this format
a, b | c, d
e, f | g, i
for a 2x2 version of the Battle of the Sexes.
3. In what sense is the Battle of the Sexes a "social
dilemma"?
Consider the cross: A/a; b/b; C/c; D/d; E/e x A/a; B/b; c/c;
D/d; e/e
a) what proportion of the progeny will phenotypically resemble
the first parent?
b) what proportion of the progeny will genotypically resemble
neither parent?
If there are 7 total notes C, D, E, F, G, A, and B and if a
five-note melody is selected at random (so that all melodies
counted in part (a) are equally likely to be chosen), what is the
probability that the melody will include exactly two “A” notes, but
no other repeated notes? (A few allowable examples: AACEG, ACAEG,
DFACA, EAABC, etc.)
A restaurant has dishes A, B, C, D, E, F and G
The owners anticipate that dishes will be ordered in the
following proportions: 30% (A), 15%
(B), 20% (C),
5% (D), 8% (E),
12% (F) and 10%
(G). The number of orders placed during
the first two days of business was 75
(A), 60 (B), 50
(C), 14 (D), 20
(E), 40 (F),
and 41 (G).
State and conduct the appropriate hypothesis test
to determine whether there is...
V=[(a b), a,b E R+] with (a1 b1)+(a2 b2)=(a1a2
b1b2)and for c E R, c(a b)=(a^c b^c) is a vector space over R.
Define T:R^2 to V by T[a b]= (e^a e^b). prove T is a linear
transformation from R2 to V.
Please fill in the blanks (values of A, B, C, D, E, F, G, H, I ,
J) for the following financial statements.
The firm’s tax rate is 35.3%.
Income Statement for Fiscal Year 2015
Sales
2,000
Cost of goods sold
1,500
Gross margin
500
Selling and general expenses
300
Operating income
200
Interest income
5
205
Interest expense
21
Restructuring charges
14
Income before tax
170
Income tax
60
Net income
J
Balance Sheet, Year 2014 and Year 2015...
In how many ways can 7 people { A, B, C, D, E, F, G } be seated
at a round table if
(a) A and B must not sit next to each other;
(b) C, D, and E must sit together (i.e., no other person can sit
between any of these three)?
(c) A and B must sit together, but neither can be seated next to
C or D.
Consider each of these separately. For (c) you may NOT...