Let f(x)=ax+b and g(x)=cx+d, where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that f◦g=g◦f.
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Let f(x)=ax+b and g(x)=cx+d, where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that f◦g=g◦f.
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- Let P(X) = “x lives in Los Angeles” and the u.d. for x is all students at Cinema Club. a. Translate into symbols, “There is at least one Cinema Club student who lives in Los Angeles.” b. Using symbols, express the negation of your expression for a.Simplify the following Boolean functions, using three-variable k-maps: a. F (x,y,z) = Σ(2,3,4,5) b. F (x,y,z) = Σ(0,2,4,6) c. F (x,y,z) = Σ(1,2,3,6,7) d. F (x,y,z) = Σ(1,2,3,5,6,7) e. F (x,y,z) = Σ(3,4,5,6,7)Let l be a line in the x-y plane. If l is a vertical line, its equation is x 5a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y 5mx 1b, where b is the y-intercept. If l passes through the point (x0, y0,), the equation of l can be written as y 2y0 5m(x 2x0 ). If (x1, y1) and (x2, y2) are two points in the x-y plane and x1 ≠ x2, the slope of line passing through these points is m 5(y2 2y1 )/(x2 2x1 ). Write a program that prompts the user two points in the x-y plane. The program outputs the equation of the line and uses if statements to determine and output whether the line is vertical, horizontal, increasing, or decreasing. If l is a non-vertical line, output its equation in the form y 5mx 1b.
- Simplify the following Boolean functions using three-variable maps. a. F(x, y, z) = ∑ (0, 1, 5, 7) b. F(x, y, z) = ∑ (1, 2, 3, 6, 7) c. F(x, y, z) = ∑ (3, 5, 6, 7) d. F(A, B, C) = ∑(0, 2, 3, 4. 6)Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂Show that F(x, y, z) = xy + xz + yz has the value 1 if and only if at least two of the variables x, y, and z havethe value 1.
- 5. Let R = {1, 3, π, 4, 1, 9, 10}, S = {{1}, 3, 9, 10}, T = {1, 3, π}, and U = {{1, 3, π}, 1}. Which of thefollowing are true? For those that are not, why not? (d) 1 ⊆ U(e) {1} ⊆ T(f) {1} ⊆ S(g) {1} ∈ SSimplify the following Boolean functions using four-variable maps. PLEASE EXPLAIN IN WRITING THE STEPS AND WHAT IS GOINING ON F(A, B, C, D) =∑ (4, 6, 7, 15) F(A, B, C,D) =∑ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)Show that if f(x) and g(x) are functions from the set of real numbers to the set of real numbers, then f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).
- If A = {1, 2, 6} and B = {2, 3, 5}, then the union of A and B is4. Let N(x) be the statement “x has visited North Dakota,” where the domain consists of the students in your school. Express each of these quantifications in English. a) ∃x N(x) b) ∀x N(x) c) ˺∃x N(x) d) ∃x ˺N(x) e) ˺∀x N(x) f ) ∀x ˺N(x)ASAP. will upvote and leave positive remark Q1. Simplify the following Boolean expressions using K-maps: F(x,y,z) = x’y’ + yz + x’yz’ F(x,y,z) = x’y + yz’ + y’z’ F(w,x,y,z) = x’z + w’xy’ + w(x’y + xy’) Q2. Find all the prime implicants for the following Boolean functions, and determine which are essential: F(w,x,y,z) = ∑(0,2,4,5,6,7,8,10,13,15) F(A,B,C,D) = ∑(0,2,3,5,7,8,10,11,14,15)