Notice that h is definec this.)

Q: Complete the following proof. Given: FG FJ, HG = IJ Prove: HF = IF

A: I have provided solution in step2.

Q: Given: ABCD: DE = BF Prove: AFCE is a O. C

A:

Q: then -u is a unit in R.

A:

Q: D prove tHhat kin

A: " Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: By using caushy Rieman prove that C. Prove thatd az az ae

A: According to the given information, it is required to use Cauchy Riemann to prove that:

Q: ST. As in pid. and find the mata'z 3D 3 B such that A- BBT,

A:

Q: Give an ekample of o Pen set in R whose

A: we need to give the example of open sets whose intersection is not open. Note: Intersection of…

Q: Prove the following Cscxcotx/secxtanx=cot^3x

A: Cscxcotx/secxtanx=cot3x

Q: Suppose RC 1. prove that if B has a sup b, then A(U(B))

A: Given:- Suppose B⊂A and to be proved if B has a Sup b, then λ(ϑ(B))∩ϑ(B)=b

Q: Suppose that > ak = a and let c E R. Prove, in all the that (c-an) = gory detail necessary, = c•Q.…

A: We will give two proofs one based on partial sums and the other will be a direct proof.

Q: Prove that tr(aA + bB) = atr(A) + b tr(B) for any A, B belongs to Mn× n(F).

A: We need to prove that tr(a A + b B) = a tr(A) + b tr(B) for any A, B belongs to Mn×n(F).

Q: D. Prove that CQ = DQ 3. In the accompanying figure we are given that se(C) = without using any part…

A: In the question we have to prove that CQ=DQ

Q: By using caushy Rieman prove that ·C. Prove thatd az az e : ae

A:

Q: 2. Which piece of information is necessary to use the SSS Congruence Postulate to prove that ATRY Y…

A: Which piece of information is necessary to use the SSS Congruence Postulate to prove that ΔTRY≅ΔCAP,…

Q: S. Use the theorems and given information to show that r

A: The figure is as shown below : Given, ∠4 = (13x-4)o, ∠8 = (9x+16)o and x=5

Q: prove that: DO e de a e +6 2/3 cwhere a, b > o

A: Where a, b>0

Q: let r ∈ R\ Q. prove that for all a,b,c ∈ Q, a+br=cr iff a=0 and b=c.

A:

Q: Theorem 3: Ifconverges to l, ther any subsequence ofalso comverges to l.

A: We have given that sn converges to l. Let snk be any subsequence of sn. We need to prove that snk…

Q: 7. Consider the figure to below. Which of the following statements are correct? Select all that…

A:

Q: Part Ca):- a*t a e CCR) for all ae R sthen prove that R is commutative.

A:

Q: Let A, Be Mnxn (F). (a) Prove that if A~ B, then At ~ Bt.

A: From the given information. The matrices A and B belong to M of order nxn. It is required to prove .

Q: K is the midpolnt of GI and HI | GJ. Complete the proof that AHIK E AJGK.

A: Given,            K is the midpoint of GI¯ and HI¯ ∥ GJ¯

Q: Let c E R and suppose that an → a. Show that can → ca.

A:

Q: Show that [my] is o(ny)

A: In the question, it has to be xy instead of xy. So, we are solving the question by taking xy. To…

Q: Prove the following identity by interpreting both sides in terms of partitions: zkak(k+1)/2 I[(1+…

A: We will assume both sides of the equation as an polynomial in z  Then we will use algebraic…

Q: Csc? %3D 2cotx

A: csc2x2cotx=csc2x

Q: Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

A: According to the given information, it is required to prove that any pair of elements in H can be…

Q: Let 9={a: aER}, then T is Borel algebra.

A: Given a statement

Q: By using Caushy Riucman Prove that? e ae

A: We will use the following result :  Result : Let the function f (z) = u(x, y) + i v(x, y)  be…

Q: Let A, B, and C e M,(C) such that ВС - СВ %3D А"А prove that BC = CB.

A:

Q: Find all values of z such that cosz = 4.

A: We find all values of z such that cos(z)=4

Q: . Given: LM NO; ZLMO= LNOM Prove: LO NM Reasons

A:

Q: Use symmetry to evaluate the followingintegrals.

A: The integral is ∫-π/4π/4tanθ dθ.   Check if the function is odd or even. Substitute -θ for θ in the…

Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a<b means that a…

Q: Suppose S, T ∈ ?(V) are such that ST = TS. Prove that range S is invariant under T.

A:

Q: Given: SRIRT; T Prove: A TRS 2 A

A: In the triangles △TRS and △SUT we  get, SR¯⊥RT¯TU¯⊥US¯∠STR≅∠TSU We have to prove that, △TRS≅△SUT

Q: (a) Prove the following property: (:) - (.".)

A: Hey, since there are more than two questions posted, we will answer the first question. If you want…

Q: Let S be a 50-element subset of {1, 2, 3,...,87} and let T = {s+11 :sE S}. Prove that SnT+ Ø.

A: This is a question of Set theory, application of the Pigeon Hole Principle.

Q: If T is surjective and V = span(3), prove that W = span(T(3)). Hint: given that span(T(3)) ≤ W, it…

A:

Q: Shew that if f is Lip. then P is Cont. on X. Nale- In fact f is uni formly Conhnaue

A:

Q: (b) Prove that Cl(AU B) = ClA U CIB.

A: The closure of S may equivalently be defined as the union of S and its boundary, and also as the…

Q: Let T={(a, o): aER}, then T is Borel algebra

A:

Q: eces. To form a le, so that the a

A: It is given that, a wire of length 20 feet is cut in to 2 pieces. X+Y=20 Here, X=2πr is the…

Q: 2. Find the exact \ength af the following curvis

A: Arc length L=∫ab1+dxdy2dy

Q: Let d, a, b E N. Prove that

A: Given,  d, a, b∈ℕ To prove that if d|a+b2  and   d|a-b2, then d|b.

Q: Let R be a UFD and fx) in REX) So, 0+a € IR.. Show that claf)~ ac(f) a nonzero polynamial

A:

Q: Call an L-tile to be the following shape Prove that for any nzl, a 2" With a 1 x 1 Corner Sauare…

A: For n = 1 each of the four 2×2 checkerboards with one square removed can be tiled using one right…

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: Apply any method to prove that alb (or a nand b), which is defined to be ¬(a ^ b) is complete. Write…

A: