8. Give a "train-theoretic" proof of the Fibonacci identity: U11 = u4 · U6 +u5 · U7.

Q: Given: Z1 = 22 АВ ВЕ Prove: АС CD A

A: Definition used -            Vertically opposite angles are equal in measure.             AA…

Q: 4. Complete the following proof in the format of your choice. D. 3. Given: AB DC and AB || DC Prove:…

A:

Q: Show that AB = O, even though A ≠ O and B ≠ O.

A:

Q: 4-IN THE ADJACENT FIGURE, IF AB = AC AND DB = EC, PROVE THAT ABEC = ACBD

A: Consider the side AB as x. Since AB is equal to AC, so, AC is also equal to x. Consider the side BD…

Q: stion 12 Suppose that In 2 = a and In 5 b. Use prop

A: Suppose ln2=a and ln5=b, Given expression is We will use the following properties of log to express…

Q: 5n² is O(n³)

A: Suppose fn and gn are positive functions. We say that fn∈Ogn if there exist positive constants c, n0…

Q: © of power Use. the dufferentiabily selies to Find the sam 13 2n+1 fu) 2n+1 within its se radus of…

A:

Q: 3. If AABC-AZXY, mZA- 50, and mzC-30, what is mX?

A:

Q: * If Iz| = Re(z), then z is

A:

Q: (i),if i = j + 1)',if i = B = A-, if i +j mif i + j

A: Here we have to find the Matrix A and B then find the product according to the question, now the…

Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: 27. Show that if a > b, and a, b + 0, then b-l > a-1, provided that a and b have the same sign. What…

A: a > b  ⇒ a - b > 0 Divide both sides by ab      (a - b)/ab > 0 ⇒  1/b - 1/a > 0  ⇒…

Q: Hint: 6"du In b b. On de 30

A:

Q: Prove the A.B = B.A.

A: To prove AB = BA.

Q: 4) If FA1 AD, ED 1 AD, AB DC , and FC EB, prove FC EB.

A: Similar triangles

Q: If AB = I and BC = I use the associative law to prove A = C.

A: Given  AB= I                  ........(1) BC= I                  ........(2)

Q: If OE = OF, then AB 2 CD. %3D

A:

Q: 4. The notation a™*, where a is not zero and n is a positive integer, means A. (-a)" В. - (а") С. a…

A:

Q: 15. Choose the correct way to rewrite (B C)' using DeMorgan's Laws (Bn C)' B'UC' Bn C' B'n C'

A: our objective is to choose the correct choice.

Q: Prove or disprove: if a, b, c e N, then a2 - 6 + 4c + 2.

A: a2-b2≠4c+2 we have to prove this relation in three cases like a<b,a>b and a=b

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

A:

Q: Complete the following proof in the format of your choice. 4. Given: AB = DC and AB || DC Prove:…

A:

Q: 4. Let A C BCR. Prove A° C B°.

A:

Q: [0,1] is not countabe. صواب İhi O

A: True

Q: Show that if AB = I, then det(A) 0 and det(B) # 0.

A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

Q: When proving Ac B, you assume x e A and x e B Select one: - True O False

A:

Q: Suppose that A ¥BSCN D and x E A. Use the method of "proof by contradiction" to show that if x e C,…

A: Given data : x∈Aandx∉C To show : x∈B

Q: Prove the following. 2. If alc and a+ b = c, then alb.

A:

Q: Prove by contradiction that if m, n € Z, then m² - n is even or m-n-1 is even.

A:

Q: In AABC, m2C = 90° A, Z1 and 22 are complementary Given: Prove: 2

A: Sum of measurements of angles of a triangle is 180 degree.

Q: 2.14 Use the identity EijmEkim = daðn – dad to show that a x (b x c) (a c)b- (a b)c. %3D

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

Q: Show, with justification, that (x^2+y^2)^2 =(x^2 -y^2)^2 +(2xy)^2   is an Identity.

A:

Q: Prove by Contradiction that if    a 0, which implies  a< = b

A:

Q: 8. Prove the following (I +CD)-\C = C(I+ DC)-1 by expressing the C + CDO in two forms. i

A: To prove the below equation by expressing C+CDC in two forms. 1+CD−1C=C1+DC−1

Q: Evaluate tan 45 tan 30 + tan 60 O 1/2 O No answer text provided. O 2

A:

Q: 13. Given O0 and mZB = 62°, find mAC.

A: Here we have to find the

Q: 521 End Adi A R A-

A:

Q: The value of Az or h in Simpson's Rule is O O b-a T O b-a 2n b-a 3n O (b-a)

A:

Q: let pcoc) =e" Since). oc G C-},3)

A: The given function is Fx=exsinx, where x∈-π2,π2.  If f'(x)&gt;0 at each point in an interval I, then…

Q: 2. O, rER-1? to be, Hn e N 1+/+--- +- 1-r Shoh that

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

Q: Prove: Vn e Z,if n is odd, then 3n+5 is even.

A: Consider the provided question, To prove: if n is odd integer, then 3n + 5 is even. Proof by…

Q: 11. Show that dza;b; is equivalent to a b. ij

A:

Q: Verify the following Identities: 2. 1. (asinx + bcosx) +acos x-bsinx) =a*+b° 2.

A:

Q: Under what conditions on A and B is (AB)-1 = A-1B-1? Prove your assertion

A: Assertion: If A and B are commutative, then  AB-1= A-1B-1.

Q: Q1: Prove that ; If CE AB, D E AB and C# D, then CD = 2 %3D

A: Key point: 1. There is only one line possible from two distinct points.2. The line is expressed in…

Q: 3.1 Prove: For all a and B in R, Ja + B] > | |a| – |B||. Hint: la + B] = |a – (-B)|-

A: Answer is in below steps.

Q: 2. Expand the following: (i) apxi (ii) 7 (√ga') (iii) A Bi

A: To expand: (i.) aijxj (ii.) ∂∂xigai (iii.) AikBi