Let A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5, 6, 7} and C = {a, b, c, d, e} 15. Give an example of f: A -> B that is not 1-1.

Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.

Note: Do not copy it from internet or else it can result it some unwanted circumstances!

Type in Latex **Problem**. Let $$A = \begin{bmatrix} .5 & .2 & .3 \\ .3 & .8 & .3 \\ .2 & 0 & .4 \end{bmatrix}.$$ This matrix is an example of a **stochastic matrix**: its column sums are all equal to 1. The vectors $$\mathbf{v}_1 = \begin{bmatrix} .3 \\ .6 \\ .1 \end{bmatrix}, \mathbf{v}_2 = \begin{bmatrix} 1 \\ -3 \\ 2 \end{bmatrix}, \mathbf{v}_3 = \begin{bmatrix} -1 \\ 0 \\ 1\end{bmatrix}$$ are all eigenvectors of $A$. * Compute $\left[\begin{array}{rrr} 1 & 1 & 1 \end{array}\right]\cdot\mathbf{x}_0$ and deduce that $c_1 = 1$.* Finally, let $\mathbf{x}_k = A^k \mathbf{x}_0$.  Show that $\mathbf{x}_k \longrightarrow \mathbf{v}_1$ as $k$ goes to infinity.  (The vector $\mathbf{v}_1$ is called a **steady-state vector** for $A.$)   **Solution**.    To prove that $c_1 = 1$, we first left-multiply both sides of the above equation by $[1 \, 1\, 1]$ and then simplify both sides:$$\begin{aligned}[1 \, 1\, 1]\mathbf{x}_0 &= [1 \, 1\, 1](c_1\mathbf{v}_1 +…

If A={8,12,16,20} and B={12,16,20,24,28}, what is the value of P (A and B)?

An argument is expressed in English below. The domain is the set of people attending a party. Every person who was late to the party left the party early. There is a person who was late to the party and was not happy. .. There is a person who left the party early and was not happy. The form of the argument is: x (P(x) → Q(x)) 3X (P(x) ^ ¬R(x)) .: 3x (Q(x) ^ ¬R(x)) Select the definitions for predicates P, Q, and R. P(x): Pick Q(x): Pick R(x): Pick

write a C++ program to Given a matrix of dimension m*n where each cell in the matrix can have values 0, 1 or 2 whichhas the following meaning:0: Empty cell1: Cells have fresh oranges2: Cells have rotten orangesSo we have to determine what is the minimum time required so that all the oranges becomerotten. A rotten orange at index [i,j] can rot other fresh orange at indexes [i-1,j], [i+1,j], [i,j-1],[i,j+1] (up, down, left and right). If it is impossible to rot every orange then simply return -1.Examples:Input: arr[][C] = { {2, 1, 0, 2, 1},{1, 0, 1, 2, 1},{1, 0, 0, 2, 1}};Output:All oranges can become rotten in 2 time frames.Input: arr[][C] = { {2, 1, 0, 2, 1},Tahir Iqbal Department of Computer Sciences. BULC{0, 0, 1, 2, 1},{1, 0, 0, 2, 1}};Output:All oranges cannot be rotten.Below is algorithm.1) Create an empty Q.2) Find all rotten oranges and enqueue them to Q. Also enqueuea delimiter to indicate beginning of next time frame.3) While Q is not empty do following3.a) While delimiter in…

Determine whether each of the following functions f : {a,b,c,d} -> {a,b,c,d} is one-to-one and/or onto.  (a) f(a) = b, f(b) = a, f(c) = b, f(d) = c (b)  f(a) = b, f(b) = b, f(c) = d, f(d) = c (c)  f(a) = b, f(b) = a, f(c) = c, f(d) = d (d)  f(a) = d, f(b) = a, f(c) = c, f(d) = b (e)  f(a) = c, f(b) = d, f(c) = a

Let L = { w | w cannot be written as st#ts with s, t  {a, b}* }. Show that L is not regular.

2. Write a function that multiplies a polynomial by a constant (or scalar). scale :: (Num a, Eq a) => a -> Poly a -> Poly a For example: > scale 2 (P [-1,0,1]) P [-2,0,2] > scale e (P [0,0,2]) P[]