4) Consider the collection of intervals on the real line: B = { (a, b) | a < b and (b – a) > 1}. Is this a basis for a topology on R? If so, prove it. If not, explain why not.

Q: Note : m=0 , Weight: 1.25 k he weight of your laptop in gram. What is its weigh

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to...

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Q: find the result and reminder

A: The given polynomial is mx2-nx+3x4+x23-6 put m=0, n=0 0x2-0x+3x4+x23-6=3x4+x6-6 we need to divide it...

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Q: SaX-とて use Gamma zax-X az -a How did he get the hypothesis?

A: To prove: 2ax-x2=a2-x-a2  

Q: Exercise 10. Let Z be the set of integers and R be the relation on Z defined by: aRb if and only if ...

A: Let ℤ be the set of integers. R be the equivalence relation defined on ℤ by , aRb ⇔ a2 ≡ b2mod 5 Fir...

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A: Let's consider the seven non digit numbers are: 3, 4, 5, 6, 7, 8, 9.   A four digit number and three...

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Q: (- 25х3 + 3х — 5) - (5х2—4х + 2) Find the quotient and the remainder :

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Q: Q1: - Find 2 of the following functions dx 2y = (z+)(z-+ 1)* a.

A: Since you have posted a multiple question according to guildlines I will solve first question(a)  fo...

Q: Solve this 75 + 75.175 -110 -25.882 If your answer is 66.06 and you can prove to me that the answe...

A: 75+75.175-110+25.882 =(75+75.175+25.882)-110 =176.057-110

Q: dy Q1: - Find of the following functions dx y = (x +) (x –+ 1 a. %3D - x2+3 b. y = %3D (x-1)3+(x+1)3

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Q: Find the Laplace transform of the following: -. f(t) = e3t

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Q: A raccoon walks from A = (0, 0) by going either one unit right or one up at each grid point. Which o...

A: Racoon walks from (0,0) according to flipping of coin either on unit right or one unit up.Now the pr...

Q: 1. f(t) = e3t 2. f(t) = t3 3. f(t) = cosh(3t) %3D 4. f(t) = cos(2t) 5. f(t) = sin(5t) cos(5t)

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Q: Is it possible for a matrix to be both upper triangular and lower triangular? Oa. Yes O b. No

A: Solution

Q: 5. Use truth tables to verify the commutative laws a) p Vq =q V P b) p^q =q^ P

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Q: te", 0st<1 (i) : f(t)= (0, t21

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Q: The open Newton-Cotes quadrature rules use equally spaced points that do not include the endpoints. ...

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Q: For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. 3 3 1 A = -9 -...

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Q: Recall that Log corresponds to the principal argument. What is the real part of Log(-3+3i)? What is ...

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Q: 4. Simplify the following: Note: m=2 n=7 (x³ y* z=7)(m+4) x" Vy4 z² (x³ y6)0 х3 у -2 z7 х уZ

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Q: 23219 Compute 11 mod 3. Show your work and justify each step.

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Q: 10 2. F (s) s2 +4s+4

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Q: f(t) = e3t f(t) = t3 %3D

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Q: Profession Percent who voted | Percent in each profession Professional 84 12 White collar 73 24 Blue...

A: let professional , white collar , blue collar , unskilled , farmer and housewife are represented by ...

Q: substitution. Sketch and label the associated dr 1. Í -2 sine

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Q: Given the argument: All dogs are animals. Some dogs are hairy. Therefore, all animals are hairy. Wri...

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Q: Determine the second derivative of f (x) = x²e* at x = -2 with a step-size of h=0.50 using Central d...

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any sp...

Q: Surface area of Revolution 1. Find the area of the surface obtained by rotating the curve y? = 4x + ...

A: Since you post more than one non interlinking questions, so as per our guideline we can solve only f...

Q: Let the relation - on the natural numbers N be defined as follows: if n is even, then n ~ n + 1; if ...

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Q: 5. Given the following utility function U(€1, c2) = [ac{ + (1 –a)c?]/ a. Find U, and U', and explain...

A: Note that this is a multipart question having 2 or more interrelated subparts. As per the company po...

Q: 2) Find volume from above Z = 14-a-yz below Z=o inside 2+y%=|

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Q: 5x+1 Q2:- Find the tangent and normal lines of the curve y: at X=1 2vx %3D

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Q: Exercise 3.5.6 Show that if H is a normal subgroup of G, then the map n:G→ G/H defined by T(g) = gH ...

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Q: 3. Let d(x, y) := |2 - 2| for x, y E R. . is a metric on R. Show that (R, d) is not a complete metri...

A: Cauchy sequence: A sequence x1, x2, x3, ... in a metric space (X, d) is called Cauchy if for every p...

Q: Find the reflection of the straight Line X+3y =1 With a circle x+y"-2X-49+1 \

A: The standard form of a circle is defined as follows: x2+y2+2gx+2fy+c=0 The center is given as -g,-f ...

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Q: Write the following in terms of factorials. 1. number of arrangements in a row of 8 objects taken 6...

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Q: . Find the solution 2 SP dt 5t³S³ Determine the general solution of dx =1+ 3y tanx.

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Q: Testing for Linear Independence In Exercises 41-48, determine whether the set of vectors in P, is li...

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Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: Proof by Induction 1 Prove by induction that 1 + 2-3 1 + n(n +1) for all integers n >1. 1.2 n+1

A: We can solve this by induction

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A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z) sub...

Q: Show that the centre of a ring R is a sub ring of R. And also show that the centre of a division rin...

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Q: (ii): f(t) = sin (t + 7)+ e³' cosh 5t

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Q: Exercise 3.3.2 Find all left cosets of the subgroup H={1, 11 (mod 20)} in the multiplicative group Z...

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Q: VII. Find I = dz (Rez)? (Im z)? where C is the upper half of the ellipse = 1 from + 2 to -2. 9 This ...

A: The complete solutions are given below  

Q: Relations and Mapping Diagrams Let A = {1, 2, 3, 4} and let B = {1, 2, 3, 4} a) Enumerate A × A b) L...

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