Question

2. Let A = {p, q, r, s}, B = {k, l, m, n}, and C = {u, v, w}, Define f : A→B by f(p) = m, f(q) = k, f(r) = l, and f(s) = n, and define g : B→C by g(k) = v, g(l) = w, g(m) = u, and g(n) = w. Also define h : A→C by h = g ◦ f. (a) Write out the values of h. (b) Why is it that some x ∈ A has h(x) = u? Explain in terms of f and g.

Answer #1

Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?

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 sample space is S = {m, n, q, r, s}. Identify two events as U
= {m, q, s} and V = {n, q, r} . The probabilities of some of the
outcomes are given by the following table:
Outcome
m
n
q
r
s
Probability
0.18
0.16
?
0.24
0.21
a. Determine what P (q) must be.
b. Find P (U) .
c. Find P (V)
(2) After creating the sample space for tossing three
coins, please answer the...

10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the edge set?
Construct a bipartite graph with vertices Q,R,S,T,U,V,W such
that the degree of S is 4.
What is the edge set?
12.-Construct a simple graph with vertices F,G,H,I,J that has an
Euler trail, the degree of F is 1 and the degree of G is 3.
What is the edge set?
13.-Construct a simple graph with vertices L,M,N,O,P,Q that has
an Euler circuit...

Read the following cases and decide the right
supplement for each case. Highlight the supplement name by finding
the word from the given box. Follow the given
example:
Example: Naif
has an infection. He needs an antibiotic
Maryam cannot digest milk. She needs to have ___lactase______
supplements
Majid is overweight. He decided to buy _________ supplements to
help him lose weight.
Muntaha’s nails always breaks so easily. She wants to get
_________ supplements.
Munther face looks older than his age....

Write a C++ program to demonstrate thread synchronization. Your
main function should first create a file called synch.txt. Then it
will create two separate threads, Thread-A and Thread-B. Both
threads will open synch.txt and write to it. Thread-A will write
the numbers 1 - 26 twenty times in nested for loops then exit. In
other words, print 1 - 26 over and over again on separate lines for
at least 20 times. Thread-B will write the letters A - Z...

True or False? No reasons needed.
(e) Suppose β and γ are bases of F n and F m, respectively.
Every m × n matrix A is equal to [T] γ β for some linear
transformation T: F n → F m.
(f) Recall that P(R) is the vector space of all polynomials with
coefficients in R. If a linear transformation T: P(R) → P(R) is
one-to-one, then T is also onto.
(g) The vector spaces R 5 and P4(R)...

A function f”R n × R m → R is bilinear if for all x, y ∈ R n and
all w, z ∈ R m, and all a ∈ R: • f(x + ay, z) = f(x, z) + af(y, z)
• f(x, w + az) = f(x, w) + af(x, z) (a) Prove that if f is
bilinear, then (0.1) lim (h,k)→(0,0) |f(h, k)| |(h, k)| = 0. (b)
Prove that Df(a, b) · (h, k) = f(a,...

Perfect competition in Q and L(Short Run), if P=200,
Q=2L^(0.5)k^(0.25), w=10, r=10;
Find values of Q,L and K.

Write a program of wordSearch puzzle that use
the following text file as an input. The output should be like
this: PIXEL found (left) at (0,9). ( Use
JAVA Array ) .Please do not use
arrylist and the likes!
Hints
• The puzzle can be represented as a right-sized two-dimensional
array of characters (char).
• A String can be converted into a right-sized array of characters
via the String method toCharArray.
. A word can occur in any of 8...

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