Let a E R which expressions are correct? and give the justification why they are part of the Borel o algebra, B(R) {a} af REN U tar}, as is rational IEN U tai}, az is rational iEN {a} 1 ,a + {a} a+ nEN n€N U {a;}, a; is rational U {a;}. %3D %3D , a; is irrational ieN iEN

Q: 1. Consider the set V of all polynomials of degree two or less, along with the following definitions…

A:

Q: complex numbers then prove that If a, az, . . ..a, and b,, b, . .., b, are |a,5, + a,b, + ..+a̟ b̟²…

A:

Q: Which is an example of two differnt fuctions that have the same domain and the same range, but have…

A: 1)Let f(x)=x+1, g(x)= square root of xSketch the graph of the function as shown below

Q: show IBat = (at 5) (1+i) (a+bi where 9,6 Are reals Hense tEs Find the value 2 (9-31) (a43i) 15-51)

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Q: be the map O Let f Sending cach Complex number

A: The detailed solution is as follows below :

Q: Exercise 10-6. Let u= (12) and v= (12345). Find vuv-¹, v²uv-2, and ບ°uv3.

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Q: Prove that for operators A and B which commute with their commutator [Â, Â]= Ĉ, so that [Â, Ĉ]=[ B,…

A: Given that A⏞,B⏞ commute with their commutator C⏞. Now, ekA.Be-kA=B+kA,B+k22!A,A,B+k33!A,A,A,B+...…

Q: Let R is ring of real numbers and *, (2) O defind on R^2 as follows, (a, b), (c, d)ER^2 then (a, b)*…

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Q: 6 - Vx + 2 = x + 2

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Q: Simplify the statement (p' v q)' v (p ^ (r v r')') v (p ^ q) using the laws of Boolean algebra.

A: Solution:Given         (p'∨q)'∨(p∧(r∨r')')∨(p∧q)To simply the statement using laws of Boolean…

Q: -2/2] and B 2 2 3) If A= 2/2 2 Show that A and B 2 commutative.

A: To show: The matrix A and B are commutative. Given information: The matrix are A=2-2222 and B=222-22…

Q: Given that x, y, and z . Prove that if (x^2)|y and (y^3)|z, then (x^6)|z

A: Solution: The objective is to prove that the given statement

Q: Please help quick thanks

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Q: What is the Cartesian product of A = {1, 2} and B = {a,b,c}?

A: Given A = 1, 2   and   B = a, b, c

Q: Prove that for all real numbers Ex)y= -(1u)

A: We have to prove that for all real numbers (- x)y= - (xy)

Q: 1. Hewrite fis) h that the mate a iend 43/6-3) 2 le your awer from part tical tes for fia) A-3 ) -3

A: Solution is given below:

Q: if A = | メ %3D Hint A = B %3D -3 B = %3D 1) find x and y 2) The muti Plicative inverse of matrix B

A: Multiplicative Inverse  The multiplicative inverse of a matrix  is equal to the identity matrix when…

Q: If a and b are in R^n, is −a in span{a , b }?

A: Let a,b∈ℝn

Q: Let X= a, b, c, d, and classify each of the following as -algebra or not justifying all your…

A: Here X = {a, b, c, d}    Any collection à of subsets of X is a σ-algebra if it satisfies following…

Q: Usina rules of differentadion to find the detvative Of the functian メ-5ゃーメ %3D It eX

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Q: 4x-3=8 identifying terms of 'x)' c) Vanable d) operotor a) coefficient b) constan

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Q: How do I prove that A∖(B∩C)=(A∖B)∩(A∖C)?

A:

Q: 16) 4j(3 – 9j) + (5j + 2)

A: Given:4j3-9j+5j+2

Q: 6) is {[a], [b], [c],[ b, c]} Complex? Explain your answer. on abstract simplice

A: 6) No, {[a], [b], [c], [b, c]} is not an abstract simplicial complex because it violates the closure…

Q: 16. a) AB Let A = [1 2 3] -1 5 3] and B 01 1 2 -25 0. Find 0 b) A+B

A: A=[1−230−15],B=[01−1120−250]

Q: Question is attached, Thankyou

A: Let us take z = x + iy.

Q: anx ; and an [a, b] ⇒ flan) → f(x) ;ant an[a,b]

A: The given statement is related to sequence.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.