Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let...
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let f : A → B and
g : B → A be defined as follows: f = {(a, c), (e, e), (g, d)} g =
{(c, a), (d, e), (e, e), (f, a), (g, g)}
(a) Consider the composed function g ◦ f.
(i) What is the domain of g ◦ f? What is its codomain?
(ii) Find the function g ◦ f. (Find...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of
the following elements:
A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x
∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J =
R.
Consider the relation ∼ on S given...
9. Let S = {a,b,c,d,e,f,g,h,i,j}.
a. is {{a}, {b, c}, {e, g}, {h, i, j}} a...
9. Let S = {a,b,c,d,e,f,g,h,i,j}.
a. is {{a}, {b, c}, {e, g}, {h, i, j}} a partition of S?
Explain.
b. is {{a, b}, {c, d}, {e, f}, {g, h}, {h, i, j}} a partition
of S? Explain. c. is {{a, b}, {c, d}, {e, f}, {g, h}, {i, j}} a
partition of S? Explain.
Let G be a group
containing 6 elements a, b, c, d, e, and f. Under...
Let G be a group
containing 6 elements a, b, c, d, e, and f. Under the group
operation called the multiplication, we know that ad=c, bd=f, and
f^2=bc=e. Which element is cf? How about af? Now find a^2. Justify
your answer.
Hint: Find the
identify first. Then figure out cb.
Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.11,...
Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.11, P(d) =
0.11, P(e) = 0.18, and P(f) = 0.19. Let E = {b, c, f} and F = {b,
d, e, f}. Find P(a), P(E), and P(F).
1. Let D={1212,1515,1717}, E={1212,1414,1515,1616} and
F={1111,1313,1414,1515,1717}.
List the elements in the set (D∪E)∩F.
(D∪E)∩F=
2. Let...
1. Let D={1212,1515,1717}, E={1212,1414,1515,1616} and
F={1111,1313,1414,1515,1717}.
List the elements in the set (D∪E)∩F.
(D∪E)∩F=
2. Let U = { 1,7,9,11,13,16,17,18,19}, X = {7,11,16,18}, Y =
{7,9,11,13,16}, and Z = { 1,7,9,18,19}. List the members of the
given set, using set braces.
(X∩Y′)∪(Z′∩Y′)
(X∩Y′)∪(Z′∩Y′)=
3. Use the union rule to answer the question.
If n(B) = 16, n(A ∩ B)=5 , and (A ∪ B) =17,
n(A)?
Let S = {a,b,c,d,e,f,g} and let T = {1,2,3,4,5,6,7,8}.
a. How many different functions are there from...
Let S = {a,b,c,d,e,f,g} and let T = {1,2,3,4,5,6,7,8}.
a. How many different functions are there from S to
T?
b. How many different one-to-one functions are there from S to
T?
c. How many different one-to-one functions are there from T to
S?
d. How many different onto functions are there from T to
S?
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...