Define the sets X and Y as: X = {*, +, $} and Y = {52, 67}. Use the definitions for X and Y to answer the questions.
(a) Write the set X × Y using roster notation.
Cartesian Product of set X = {*, +, $} and Y = {52, 67}. is
X x Y = {(*, 52), (*, 67), (+, 52), (+, 67), ($, 52), ($,67)}
Exercise 3.3.1: Unions and intersections of sets. Define the sets A, B, C, and D as follows: A = {-3, 0, 1, 4, 17} B = {-12, -5, 1, 4, 6} C = {x ∈ Z: x is odd} D = {x ∈ Z: x is positive} For each of the following set expressions, if the corresponding set is finite, express the set using roster notation. Otherwise, indicate that the set is infinite. (c) A ∩ C (d) A ∪...
Let X and Y be sets, A is a subset of X. Define functions f: A --> Y and F: X --> Y. Show that F is an extension of f if and only if the graph of f is a subset of the graph of F.
Defn: Let X and Y be sets. Their Cartesian product, X X Y , is the set containing all ordered pairs (x, y) with x € X and Y EY. If Y = X we write X X X = X?. 8) Show that X x 0 = 0 x X = 0 for every set X.
EXERCISE2.6.7: Cartesian products, power sets, and set operations.Use the following set definitions to specify each set in roster notation. Except where noted, express elements of Cartesian products as strings.A = {a}B = {b, c}C = {a, b, d}(a)A × (B ∪ C)
Express the system of differential equations in matrix notation x – 4x + y - (cos t)x = 0 y"+y" - t?x' + 3y'+e-2x = 0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. Xi =X, X2 = X". X3 = y, Xa =y" O B. *= x, X2 = x', *3 = y, X4 =y', X5 =y" OC. *1 =...
Consider the following two sets of scores X: 80, 70, 55, 63, 72 Y: 50, 52, 59, 60 Which of these sets of scores was more likely drawn from a population with the greater variance and why?
QUE Suppose that X and Y are sets (with at least 2 elements each) with partial orders <x and Ky respectively. Define the relation on X Y by (x), y) = (02, y2) if and only if x'j <x X2 and yiy y2. Show that is a partial order on X Y . Is it also a total order?
Write in roster notation the elements of S = {x l Exists a y such that y = (-2,-1,0,1,2) and x = y^2} A. S = {0,2,4} B. S = {0,1,4} C. S = {0,1,2} D. S = {-4,-1,0,1,4}
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the top portion of the function using Geogebra. Does the function appear to be continuus at 0? (b) Find fz(z, y) and fy(z, y) when (z, y) #10.0) (c) Find f(0,0) and s,(0,0) using the limit definitions of partial derivatives and f,(0,0)-lim rah) - f(O,0) d) Use these limit definitions to show that fay(0,0)--1, while x(0,0)-1 (e) Can we conclude from Clairaut's theorem that()-yr(x,y) for...
Solve the inequalities. Write the solution sets in interval notation if possible. 6 (a) <o y +1 6 (b) <0 y +1 (c) 20 y+1 (d) >0 y +1