1. Let A = {1,2,3,4} and let F be the set of all functions f
from...
1. Let A = {1,2,3,4} and let F be the set of all functions f
from A to A. Prove or disprove each of the following
statements.
(a)For all functions f, g, h∈F, if f◦g=f◦h then g=h.
(b)For all functions f, g, h∈F, iff◦g=f◦h and f is one-to-one
then g=h.
(c) For all functions f, g, h ∈ F , if g ◦ f = h ◦ f then g =
h.
(d) For all functions f, g, h ∈...
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) ‘
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, 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...
a) Let f : [a, b] −→ R and g : [a, b] −→ R be...
a) Let f : [a, b] −→ R and g : [a, b] −→ R be differentiable.
Then f and g differ by a constant if and only if f ' (x) = g ' (x)
for all x ∈ [a, b].
b) For c > 0, prove that the following equation does not have
two solutions. x3− 3x + c = 0, 0 < x < 1
c) Let f : [a, b] → R be a differentiable function...