a) Use truth tables to show that the following are valid
arguments:
i. [p (p → q)] → q
ii. [(p → q) ∧ (q → r)] → (p → r)
b) Use truth tables to show the logical equivalence of:
i. (p → q) ⇔ (¬p ∨ q )
ii. (¬p ∨ q) ∨ (¬p q) ⇔ p
Please answer the questions in the space provided below each
question. Show all of your work and circle your final answer.
You forecast there are three potential scenarios for the
economy: a bull, flat, and bear market. You also estimate the
returns for a stock and bond mutual fund as follows:
Economic Scenario
Stock Fund
Bond Fund
Probability of
Scenario
Recession
-18%
6%
0.3
Flat
8%
4%
0.45
Boom
20%
-8%
0.25
Using this information, you find for
the stock...
Topology question:
Show that a function f : ℝ → ℝ is continuous in the ε − δ
definition of continuity if and only if, for every x ∈ ℝ and every
open set U containing f(x), there exists a neighborhood V of x such
that f(V) ⊂ U.
Please use any of the methods to prove whether each of
the following arguments is valid or invalid. For each problem,
please identify the method that you have decided to employ and make
sure to show your work.
1. It is obvious that nuclear energy is needed. Nuclear energy
is needed if and only if solar energy cannot be harnessed. And it
is also true both that solar energy can be harnessed only if funds
to do so are available,...
5. For each set below, say whether it is finite,
countably infinite, or uncountable. Justify your answer in each
case, giving a brief reason rather than an actual
proof.
a. The points along the circumference of a unit
circle.
(Uncountable because across the unit circle because points are
one-to-one correspondence to real numbers) so they are
uncountable
b. The carbon atoms in a single page of the
textbook.
("Finite", since we are able to count the number of atoms in...
Please show how answer is derived. Assume the information below
to answer the following questions:
(1) If you use covered
interest arbitrage for a 90-day investment, what will be the amount
of US dollars you will have after 90 days?
(2) What is the percentage
gain or loss on an annual basis?
Amount of investment
$5,000,000
Current spot rate of pound
1.28
90-day forward rate of pound
1.25
3-month deposit rate in US
2%
3-month deposit rate in UK
3%
Subject: Statistics
Please show complete work for the multiple-choice
questions below
1. If the mean and median are equal, you know
that the:
a. distribution is symmetrical
b. distribution is skewed
c. distribution is normal
d. mode is equal to the median
2. The mean, median and mode are all measures
of:
a. the midpoint of the distribution
b. the most common score
c. percentile ranks
d. variability
3. Which of the following characterizes the
mean?
a. The sum of...
Question 1 - Infinite Sequences.
(a). Determine an infinite sequence that satisfies the following .
. .
(i) An infinite sequence that is bounded below, decreasing, and
convergent
(ii) An infinite sequence that is bounded above and
divergent
(iii) An infinite sequence that is monotonic and converges to 1
as n → ∞
(iv) An infinite sequence that is neither increasing nor
decreasing and converges to 0 as n → ∞
(b). Given the recurrence relation an = an−1 +...
Below Statement is True, False, or Uncertain question. Justify
the response. (Include Graph). Its a Macro economics question
Suppose the aim of the government is to increase the
economic well-being of it’s citizens. According to the
Solow-Swan model from lectures, the government should try to
increase the savings rate, as this will lead to a higher
steady-state level of capital and a higher level of steady-state
outpur, and thus will improve economic well-being