Let
E, F and G be three events in S with P(E) = 0.62, P(F) =...
Let
E, F and G be three events in S with P(E) = 0.62, P(F) = 0.58, P(G)
= 0.34, P(E ∩ F) = 0.32, P(E ∩ G) = 0.19, P(F ∩ G) = 0.14, and P(E
∩ F ∩ G) = 0.06. Find P(EC ∩ F ∩ G), P(E ∩ FC ∩ G), and P(E ∩ F ∩
GC).
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
A = { a, b, c, d , e, f, g} B = { d,...
let
A = { a, b, c, d , e, f, g} B = { d, e , f , g}
and C ={ a, b, c, d}
find :
(B n C)’
B’
B n C
(B U C) ‘
1.Given that P(E) = 0.32, P(F) = 0.32, and P(E ∩ F) = 0.18. Find
P(E...
1.Given that P(E) = 0.32, P(F) = 0.32, and P(E ∩ F) = 0.18. Find
P(E ∪ F).
a) 0
b) 0.18
c) 1
d) 0.54
e) 0.46
f) None of the above
2. Given P(A) = 2⁄5, P(B) = 19⁄50 and P(A ∩ Bc ) = 1⁄5. Find P(A
∩ B).
a) 0.16
b) 0.26
c) 0.98
d) 0.20
e) 0.40
f) None of the above.
3. Suppose P(E) = 57⁄100 , P(Fc ) = 7⁄20 , and P(F...
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 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 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...
Let f(x)= a -bx^c + dx^e where a, b,c,d,e >0 and c<e.
Suppose that f(x0)= 0...
Let f(x)= a -bx^c + dx^e where a, b,c,d,e >0 and c<e.
Suppose that f(x0)= 0 and f '(x0)=0 for some x0>0. Prove that
f(x) greater than or equal to 0 for x greater than or equal to
0