Let f: R → R be given by f (x) = (x − 1)². Prove that f(x) is neither one-to-one nor onto.

Q: Let S be a set of n lines in the plane such that no two are parallel and no three meet in the same…

A: Let S be a set of n lines in a plane such that notwo are parallel and no three meet in the same…

Q: X = {-3, -2,-1,0, 1}. Let f: X e range of the function is

A: From question , Given X = {-3,-2,-1,0,1} f(x) = |7x+11|

Q: For f(a, b) = (a | b) | b (a) Simplify f(a, b). (b) Find DNF for f(a, b). (c) Is f(a, b)…

A: (a) f(a, b) = (a | b) | b can be simplified as follows: f(a, b) = (a | b) | b = b | b (since a | b =…

Q: f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).

A: Proof: given: f:R---->R g:R----->R f(x) is O(g(x)) so we can say |f(x)|≤c|g(x)|.........(1)…

Q: DO A K-MAP FROM THE EQUATION BELOW: F=E'.(B'+D)+(E+D)

A: Given  F=E'.(B'+D)+(E+D) Truth Table:   B D E B' + D E + D E'.(B'+D) F=E'.(B'+D)+(E+D) 0 0 0 1…

Q: Given the function f (a, b, c, d) = ∑m(0,2,10,11,12,14,15) + ∑d(1,8,13), how many X don't cares are…

A:

Q: Find the symmetric closure of R.

A: Given To know symmetric closure of R.

Q: Given the domain of each function is Z x Z and codomain of each function is Z. Categorize the ff.: f…

A: Solution:   Given,

Q: 5. Based on the truth table, use a K-map to find a minimal Sum of Products expression. Show your…

A: given:-  truth table utilizing a Karnaugh Map (K-map), we first need to make the K-map for the given…

Q: Implement the fumction F(A, B, C, D) = Em(1, 2, 5, 7, 9, 14) using MUX. %3D

A: Since the size of MUx is not specified, we can use any size. So for sake of simplicity let's use 8x1…

Q: Prove the argument(∀x)[(B(x) ∨ C(x)) → A(x)] → (∀x)[B(x) → A(x)]

A: Given argument, (∀x)​[(B(x) V C(x)) → A(x)] → (∀x)​[B(x) → A(x)]

Q: Prove or disprove that for any x ∈ N, x(x+1)/2 ∈ N (where N = {0, 1, 2, 3, ….}

A: Hello student

Q: Discussion: Minimize the following function in SOP minimal form using K-Maps And draw the output…

A: Explanation: The SOP K-Map for the given expression is: Therefore, f = AC'D' + A'D + A'C + AB

Q: Use two different ways to prove XY + Z= (X+Z)(Y+Z). a) Purely Algebraic way p) K-map

A: (X+Z).(Y+Z) =X.(Y+Z) + Z.(Y+Z) =X.Y +X.Z+ Z.Y+ Z =X.Y+Z.(X+Y+1) =X.Z + Z.(X+1)  [Y+1=1] =X.Z + Z

Q: r=Emc Σm(1,3,5,6,7) F

A: These question answer is as follows,

Q: Prove that f(x) = x is O(x3).

A: Attached image below:

Q: Simplify the following Boolean function by a four-variable K-map in terms of minimum Sum of Products…

A: The SOP Expression is F= A’B’D’+BC’D+AC’+AB’D

Q: Given that h(p)=p2−3p+5, Find;h(x-3)

A: Given: h(p)=p2 + 3p + 5 then, by putting p=x-3 h(x-3) = (x-3)2 + 3(x-3) + 5           = x2 + 32…

Q: Simplify the function f(xyz)=Sum(2,3,7).using k map

A:

Q: nvestigate the many functions that are performed by each member of the team while using the agile…

A: The Agile approach is a project management approach which  involves the breakdown of the whole…

Q: 3. Given the following minterm expansion: F(a, b, c, d) = Em(0, 2, 3, 4, 8, 10, 11, 15) Draw the…

A:

Q: For the function f: Z Z prove or disprove whether f is injective and/or surjective f(x) = 4x –6 %3D

A: A function is injective if every element of the range having an image of at least one element of the…

Q: Reduce the following using K-Map. Obtain using Sum of Product. 1. Σ(0,2,3,4,5,7,10,11,13,14,15)

A: Karnaugh presented a simple approach for simplification of Boolean functions. The Karnaugh map…

Q: e define that a function f(n) has an upper bound g(n)

A: Big O notation The function  f(n) = O(g(n)) is defined when the following two properties hold: There…

Q: Simplify the following function: F (W, X, Y, Z) = ∑ (3, 5, 11, 15) with don't care conditions d =…

A: Given  F (W, X, Y, Z) = ∑ (3, 5, 11, 15)   and don't care , d = ∑(1, 2, 6, 9)

Q: The Boolean function ?(?, ?, ?, ?) = ∑ ? (0,5, 7, 8, 9,11)   Generate the Truth Table and use…

A: Solution:

Q: We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now…

A: The solution is given below for the above given question:

Q: Let X = {-3, -2,-1,0, 1}. Let f: X→ N by f(x) = |7x + 11 The range of the function is

A: In given question, we are asked the range of the given function f. We are given set X and a function…

Q: Reduce the following using K-Map. Obtain using Sum of a Product 1. Σ (6,8,9,10,11,12,13)

A: Karnaugh presented a simple approach for simplification of Boolean functions. The Karnaugh map…

Q: 3. Write out the canonical form of the following function. Draw the K-Map and give the minimized…

A: Given the F(A,B,C) , we have to draw the K-map for this and find the Essential prime implicants and…

Q: Let E : y2 = x3 + 3x + 4 be an elliptic curve over F37.   1, Find all the elements of the…

A: Below is the complete answer with explanation in detail for the given question.

Q: S.O.P F(A, B,C, D) = E( 4 , 5 , 7 , 6 , 8 ,9 ) using P.O.S Karnaugh map.

A: Change the sign to ∏.The missing terms are 0, 1, 2, 3, 10, 11, 12, 13, 14, 15. Fill the K map as…

Q: Find a basis for and the dimension of the subspace w of R4. w = {(0, 4t, t, -t): t is a real number}…

A: Given: Sub-space W of R4 is = {( 0, 4t, t , -t ) : t is real numbers}

Q: We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now…

A: See below step for code.

Q: For each of these functions, determine its domain, codomain, and range.    f: Z → R, f(n) = 7

A: Domain is.  Z Codomain is R Range is 7

Q: c,d 00 01 11 10 a,b 00 1 1 1 01 11 10 1 1 1

A: Layout : Groups : d` = (0,2,4,6,8,10,12,14) b`.c` = (0,1,8,9) Expression : F= d` + b`.c`

Bounded Summation

In mathematics, the summation is the process of adding a sequence of numeric values, known as addends and their result is called sum or total. The term summation refers to the addition or sum of two or more numbers or units. For example-