6. Determine whether each of these statements is true or false. а) х€ {{x}, {x, у}, (x, у, 2}} b) {x} C {x} c) {x} E {x} d) {x} E {{x}} e) Ø C {x} f) Ø E {x}

Q: b. Prove that coth² x-1=csch?x

A: Sinh(x)= (e^x-e^-x)/2. Cosh(x)=(e^x+e^-x)/2

Q: Attention: For the sidework in photo1, the step I circled is wrong and needs to be reviewed using…

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Q: Show that a fomws with R>o Ssee igue] may be descuibed panometuicaly by u cU,N] Cosu, (R+ o…

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Q: Prove that (C, +) ≈ (R × R, +).

A:

Q: The projection of u onto v is given by projvu = ________.

A: The projection of u onto v is given by projvu = compvu.

Q: Show that : sup {reQ:r<a} =a, for each a e R. %3D

A:

Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

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Q: Disprove the following by countererample and please provide justification for each line of proof.…

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Q: if f is derivable in [a, b] and f' (a) not equal to f' (b), then for each number k lying between f'…

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Q: ATOM = AVER and mZT = 83, mZR=32, TM = 10, RE = 14.Complete the congruence statements and find the…

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Q: 16. Write a two column proof. Given: OSTUV U V. Prove: AVXS = AUXT T S 8.

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Q: 1/3 If (x+iy) =a+ ib, Prove that

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Q: Let A,BE Mmna Shaw that vTAw= V' Bw for all VER™ end WEIR" if and only if LA=B. %3D

A:

Q: Dyani wrote a proof to show that ZXWY ZYZX. What is her error? Since ZWXZ LZYW, LXZW LYWZ, and XW…

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Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

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Q: Let x and y be non-negative reab· show that, use Proof by Contradietion X+4 2

A:

Q: 27. Prove in detail that Q(/3+ 7) = Q(/3, v7).

A: We have to prove given equation.

Q: 5. Prove that if x, y ER, then x + y ≤ x + y. Use the following cases: (i.) x, y ≥ 0, (ii.) x, y <…

A: We now prove that if x,y ∈ ℝ , then x+ y≤ x+y with the help of given three cases.

Q: Prove that AXY Z2 AZW X. X Y W Z Statement Reason 1 MLZXY MZXZW Given Pick statement v Given 3 XZ =…

A: Reflexive property means common side

Q: メ人 xp- Vtan (e) sec?(e) de Evewale Jhe Jollowing! op (e)as (a)

A:

Q: . Use a two-column proof to prove the equivalence below -(PV-Q) v (-P A-Q) = ¬P

A:

Q: 6. Prove: 4 |x – y| 0, then x = y Vx, yER

A: To solve Q.6 Prove: If x-y&lt;ε, ∀ε&gt;0, then x=y ∀x,y∈ℝ If (Given) Then (To prove) ∀ε&gt;0,…

Q: 20. Let -(). -- (). (). u = w = If au + yv = w. (x, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2…

A: To find  The value of x-y

Q: 7) Assume dim V = n, dim U = k, dim W = n - k, and U + W = V. Prove that Un W = {0} and V = U OW.

A: Given, dim V=n, dim U=k. dim W=n-k, and U+W=V.To prove that  U∩W=0 and  V=U⊕W.

Q: Suppose X has n elements and Y has m elements. How many bijections X → Y are there?

A: To find: The number of bijections X → Y are there. Given information: X has n elements and Y has m…

Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: 1. Decide if the following statement is True or False: %3D Let A1, A2, ..., Ak E Mnxn(R) be such…

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Q: Prove: For allintegers aandb, if a|b then a² |b²

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Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

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Q: Complete the proof that AWXY AWYX. Y W Statement Reason WX WY Given ZW ZW AWXY AWYX AAS ASA CPCTC…

A: see below the answer and explanation

Q: Find propositions P(x, y) and Q(x, y) that demonstrate tha (Vxay, P(x, y)) A ay, Q(x,y)) is…

A: Let Statement 1: ∀x∃y, Px,y∧∀x∃y, Qx,yStatement 2: ∀x∃y, Px,y∧Qx,y

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

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Q: Show that (t As) can be derived from the premises pq, q→~r,r, pV (t As).

A:

Q: 9. Prove that the following pair of formulas are equivalent in SDE. U → -(E V D), (-E A ¬D) →¬U

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Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

Q: Ju 20²u c² of2 (r, t) = u(x,0) = 0, ut(x,0) = 0 u(0,t) = 0 u(1,t) = 0. da2(x, t) + XX , 00,

A: Introduction: The basic method to solve a partial differential equation is the method of separation…

Q: Solve the BVP on interval Lo, nJ) 2 %3D 2.

A:

Q: 4) Let (an) be anumsenical seguence sveh that lin u"4, Then the nadius of Comvergonce of the beries…

A: The given series is: ∑n=0∞7an2xn. We will use the root test to find the radius of convergence.

Q: If ge R [a,6] 'ib h) < gcx) exapt gex) except for a finite number 8 points in (a, b] then prove that

A: The partition from a to b should be first divided to form a set of integrals.

Q: prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability

A: Use the deduction theorem: Deduction theorem states that, If ┌ A⊦B then ┌⊦ A→B

Q: a) Suppose that you wish to prove that ARST = ASRV. Using the reason Identity, name one pair of…

A: Given: We wish to have the triangle RST and triangle RSV to be congruent.

Q: Given: STaVU T. Prove: 4SVTZUTV

A:

Q: Dyani wrote a proof to show that ZXWY ZYZX. What is her error? Since ZWXZ LZYW, ZXZW LYWZ, and XW…

A: Explanation of the answer is as follows

Q: show that fo=Ixl is Conlindalus everyuhere

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Prove Vr, y E Z, if ry is even and y is odd, then r+y is odd.

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Q: prove that for operatrs a and b which comute with thier commuters[a,b]=c,so that [a,c}=[b,c}=0 ,…

A: We know that ekABe-kA=B+kA,B+k22!A,A,B+... Given that A and B commute with their commutator then…

Q: Complete the proof that AUWX AWUV. Statement Reason VW 1 UV Given UX 1 WX Given w/

A: Given:  VW⊥UV UX⊥WX UV∥WX In △UWX and △WUV ∠X=∠V              (All right angles are congruent)…

Q: Suppose AnB CC\D and x E A. Prove that if x eD then x ¢ B. (Hint: prove via contrapositive)

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Q: Suppose that B is a point between A and C. Prove that AB−→ =AC−→

A: B is a point on AC. Let, A=(x1,y1) and C=(x3,y3)Then direction vector of AC=(x3 - x1, y3-y1)