(b) Give examples of subsets A and B of IR" to show that the equation a(AN B) = DAn aB is not true in general.

Q: Solve the following inequality graphically in two-dimensional plane:y < – 2

A: We first draw y=-2 line

Q: 5. Prove Theorem 5 using the Linear Pair Axiom.

A:

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: ?, R(A)IN(A*)

A:

Q: nts A and B have symmetry with respect to the ) (9, 2) (х, у) %3D -) (0, 8) (x, y) =

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: 23. Prove that (xo, Yo), (x1, y1), and (x2, y2) lie on a line if and only if (х — Хо)02 — Уо) - (*з…

A:

Q: find Len th of avectors 2く3,-S,\> D=くW5> ビ,37 andd And Draw the coordinates for each point

A:

Q: (ii) AU(BnC)= (CUB)NĀ. %3D

A: Introduction :

Q: Question 5 Use the Cauchy-Schwarz inequality to show that if a1, a2, . .. , an are positive real…

A:

Q: spectra of TT* and T*T are real and cannot

A:

Q: b, c e R such that abc

A:

Q: Discuss the cosets of { (x, y) | x, y E R, x = y } in (R × R, +).

A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: 2:31 AA A learn-us-east-1-prod-fleet01-xythos.c C Section 3.2 Homework (from the 5" Edition) 1. Let…

A: 1.(i) we have x,y and z ∈R           and R  is a feild with respect to addition and multiplication…

Q: A designer is creating various open-top boxes by cutting four equally-sized squares from the corners…

A: Given that, a square of sides x length is cut from each corner of the sheet. Then the length and…

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: The distance from the point K(3, -2, 0) to the az- plane is Select one: O-2 O √13 O 0 02 O None of…

A:

Q: 3. Find the constants bo, co, a1, b1, C₁ so that So(x)=1+ box + cox² + x³, S(x) = { S₁(x) = a₁ - 2x…

A:

Q: If the conditions of the fixed point theorem are not satisfied, then there exist no unique fixed…

A: The ciric theorem states that, Let X be a complete metric space, and let f : X → X be such that,…

Q: Find all numbers z such that Az + Bz² + Cz = D [2 4 21 li 3 B=[i 1 1. A = -2 -1 [2 4 2] C = 1 3 1 -1…

A: Find all numbers z such that Az3 + Bz2 + Cz =D Given matrices,                              A=242131…

Q: 2 Let A B = -1 |0 and C = 7 Find x, y,z | 2 -3 such that AB =C.

A:

Q: Find all the values of x in the interval [0,2pi], that satisfy the question.  10cos(x)+5sin(2x)=0

A: Given equation is Solve the given equation for x

Q: 3) Given: BAC= AHC=90°. %3D Prove that: B= HAC and C= HAB. %3D %3D H. C

A: We will prove the given problem.

Q: 13. Prove that the three points (-3, 2, 4), (6, 1, 2), and (-12, 3, 6) are collinear by using the…

A: To solve the following problem

Q: 1. State and prove the full version of the Pythagorean Theorem

A:

Q: According to boolean algebra x.(1 + y) =?

A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c  (ii) Identity law :…

Q: (2) Let P = (1, 1), Q = (4, –2) and R = (2,3). Find the point S such that R$ is equivalent to PQ.

A:

Q: 4. Let A %3D {a, b, c}, В %3D {x, у}, and C %3D {0, 1}. Find a) АхВх С b) СхВхА с) СхАх В d) ВxВxВ.

A: Given that: 4. A={a, b, c}, B={x, y}, C={0, 1}   NOTE: As per our answering guidelines, we can only…

Q: 2.2.7. Prove the full triangle inequality: for every x, y E R", | |æ| – |y|| < |x± y| < |æ| + \y]-…

A:

Q: Theorem 2.6.9. If P and Q are two points such that P + Q, then there exists a point R such that P,…

A: Axioms used: 1. There is one and only one line that contains two distinct points. Given: Theorem…

Q: Example 3: Find real numbers x, y and z such that xi + 2yj – zk + 3i – j = 4i + 3k

A:

Q: Theorem 4.8.1 Irrationality of V2 V2 is irrational.

A: For any integer n such that n² is even then n is also even.

Q: Theorem P.3. ( Dual of Axiom P.4) Given two distinct points, there is at least one line incident…

A: It is noted that, if two points lie in a plane, then the line joining them lies in that plane…

Q: In AHIJ, HJ is extended through point J to point K, mZJHI = (x+ 12)°, (x- 3)°, and m/IJK = (5x –…

A:

Q: Question is attached, Thankyou

A: Let us take z = x + iy.

Q: Find a number z that satisfies: |z| - z = 2 + i

A: Complex number which satisfy |z|-z= 2+i

Q: 2.2.12 Prove that if x and y positive real numbers, then Vx+y # Vx+ Vy. Argue by contradiction. are

A: Let x and y are positive real numbers. Also let x+y=x+y Now squaring on both side,we get…

Q: R.2. Prove that if A and B – C are disjoint, then AN BCC.

A:

Q: a- If A = -1 %3D 2 and B = -41 prove that (A + B)T = AT + B". 12 [1/2 - If A-1 =1/2 -1/2) and |A| =…

A:

Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: Prove that R (D-1 and R)%=(-)

A: The objective is to prove that  Pn1=1Pn-1=-1n

Q: 6. 1 Let W = Span -1 4 and y = 1 What is the distance -4 1 10 from y to W ?

A:

Q: Theorem 4P.1 There are exactly six lines in the four-point geometry.   proof the Theorem 4P.1 by…

A: To prove that in the Four point geometry , there are exactly six lines: the proof should be based on…

Q: generally true? Prove / disprove this.

A: P(x+y|x)=probability of (x+y) given x. P(y|x)=probability of y given x.

Q: 1. (a) Let 5 -6 -6 B = |-1 4 2 3 -6 -4 Find oigon nigon un imil to D

A: To finding the eigenvalues and eigenvectors to the given matrix we use Gaussian elimination method.…

Q: 4. Prove the statement of 3 on page 9 of lecture notes 10, i.e., SSE xa-1)(0–1)*

A: The given model is, yij=µ+Ai+Bj+∈ij    where, i= 1, 2.......a and  j= 1, 2.....b∈ij~N(0, σ2∈)Testing…

Q: Determine the ratio and interval of con (-1)"x" in=0 n6" O R.O.C=6, 1.0.C: x E [-6, 6) R.O.C=1,…

A: Here we have ∑n=0∞(-1)nxnn6n=∑n=0∞an ⇒an=(-1)nxnn6n

Q: Prove that (a - b) x (a + b) = 2 a x b and find the geometrical meaning of it.

A: find the explanation below