5. Determine whether the following statements are TRUE or FALSE.
If the statement is TRUE, then...
5. Determine whether the following statements are TRUE or FALSE.
If the statement is TRUE, then explain your reasoning. If the
statement is FALSE, then provide a counter-example. a) The
amplitude of f(x)=−2cos(X- π/2) is -2 b) The period of
g(x)=3tan(π/4 – 3x/4) is 4π/3.
. c) If limx→a f (x) does not
exist, and limx→a g(x) does not exist, then limx→a (f (x) + g(x))
does not exist. Hint: Perhaps consider the case where f and g are
piece-wise...
1. For each statement that is true, give a proof and for each
false statement, give...
1. For each statement that is true, give a proof and for each
false statement, give a counterexample
(a) For all natural numbers n, n2
+n + 17 is prime.
(b) p Þ q and ~ p Þ ~ q are NOT logically
equivalent.
(c) For every real number x
³ 1, x2£
x3.
(d) No rational number x satisfies
x^4+ 1/x
-(x+1)^(1/2)=0.
(e) There do not exist irrational numbers
x and y such that...
Devise the synthesis of:
1- Benzene to: a) m-bromonitrobenzene; b) p-bromonitrobenzene;
c) o-chlorobenzoic acid; d) p-chlorobenzoic...
Devise the synthesis of:
1- Benzene to: a) m-bromonitrobenzene; b) p-bromonitrobenzene;
c) o-chlorobenzoic acid; d) p-chlorobenzoic acid; e)
m-chlorobenzoic acid; f) 2,5-di(n-propyl)-1-bromobenzene;
g) 2,4-di(n-propyl)-1-bromobenzene
2- Fluorobenzene to: a) p-cyanophenol (aka
p-hydroxybenzonitrile); b) p-chloroanisole (aka
p-methoxychlorobenzene); c) p-cyano-N,N-dimethylaniline
3- Nitrobenzene to: a) p-dichlorobenzene; b)
m-dichlorobenzene
1. Write the following sets in list form. (For example, {x | x
∈N,1 ≤ x...
1. Write the following sets in list form. (For example, {x | x
∈N,1 ≤ x < 6} would be {1,2,3,4,5}.) (a) {a | a ∈Z,a2 ≤ 1}. (b)
{b2 | b ∈Z,−2 ≤ b ≤ 2} (c) {c | c2 −4c−5 = 0}. (d) {d | d ∈R,d2
< 0}.
2. Let S be the set {1,2,{1,3},{2}}. Answer true or false: (a) 1
∈ S. (b) {2}⊆ S. (c) 3 ∈ S. (d) {1,3}∈ S. (e) {1,2}∈ S (f)...
3. Identify the hypothesis and conclusion in the following
statements. Then, find a counter example showing...
3. Identify the hypothesis and conclusion in the following
statements. Then, find a counter example showing that the statement
is false. Here n, m, and p are originally assumed to be
integers.
Statement 1. If m and n are integers, then
m/n is an integer.
Statement 2. If m and n are
positive integers, then m - n is a positive
integer.
Statement 3. If p is an odd prime number, then
p^2 + 2 is a prime number.
Statement...
Let the population have N=7 units, with {(unit,value)} =
{(A,-1),(B,+1),(C,-2),(D,+3),(E,-4),(F,+5),(G,-6)}. The design is
as follows: first...
Let the population have N=7 units, with {(unit,value)} =
{(A,-1),(B,+1),(C,-2),(D,+3),(E,-4),(F,+5),(G,-6)}. The design is
as follows: first choose A or B at random; if A then choose from
{C,D} at random, if B then choose from {E,F,G} at random. 1) Find
the first-order inclusion probabilities (note that the sample size
n is fixed at 2).
Verify (show numerically for this example) that the
Horvitz-Thompson estimator is unbiased for the population total.
(Hint: find the probability of each sample and the value...