Give a direct proof of the claim: Vn E N, if the last two digits of n are divisible by 4 then n is divisible by 4.

Q: Which of the following statements best justifies In(n+ 1)

A: We are given the following series.               We know that ln(x) < x. So, ln(n+1)/n will…

Q: Let x E Z and y E Z. Prove the following statement: If y = 2 mod 4, then xy 1 mod 4.

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Q: 4. In the figure, if AB = AC and BO = OC. Prove that ZB = C .C B

A: a). Given: AB=AC and BO=OC Prove: ∠B=∠C

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: If x mod 5 = 2 and y mod 5 = 3, then xy could be D 306 D 843 D 342 O 197

A: See solution below

Q: What other information do you need to prove AABD=ACBD? B A O AB = CB O ZABD=ZCDB O BD= BD O AD= CD

A: Here, we can observe from the figure that |AB| = |CB| and BD is common. Now, if we can prove that…

Q: 2. If P (n) : "2.4z + 3""" is divisible by k for all ne N" is true, then the value of k is

A: The solution is given below:

Q: Q1: Prove that ; If CE AB, DE AB and C + D, then CD = AB.

A: The given question can be solved as shown in step 2.

Q: 2. Ifr + 1, show that for any positive integer n, a + ar + ar +...+ ar" = a(rn+1 – 1) - r - 1 the…

A: we need to prove if r≠1 thena+ar+ar2+.....+arn=arn+1-1r-1let pn=a+ar+ar2+.....+arnto prove…

Q: Prove that if r <s < n, then P(n , s) is divisible by P(n,r).

A: Given: r≤s≤n Therefore, n-r≥n-s So we can write n-r! = n-rn-r-1n-r-2...n-sn-s-1n-s-2...1 n-r! =…

Q: Find a natural umber N such that if |a – 5| < e <1 then |a² – 25| < Nɛ.

A: According to our company policy, we are supposed to answer one question at a time. For the rest…

Q: Suppose that a and b are two numbers with this property: for anv e va it is true that azb. Prove a =…

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Q: Prove the following statement: "Let a, b and n be integers. If n doesn't divide ab, then n doesn't…

A: The given statement is -" Let a.b and n are integers. If n doesn't divide ab, then n doesn't divide…

Q: 1. Consider the diagram below and use a two-column proof to prove the statement. C Glven: CL I AP,…

A: Given: AP||CL and CP||AL

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&lt;b,a&gt;b and a=b

Q: O Determine rand s so that, 3.

A:

Q: 3.3. Let a, BEC. Prove that la + B2 + la – B|2 2(la|? + |B|?), and deduce that |a + Va? – B2|+ |la –…

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Q: Prove that if r < s < n, then P(n, s) is divisible by P(n.r).

A: Use the formula of permutation

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

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Q: Prove the following (by using contrapositive): Let a, b and n be integers. If n doesn’t divide ab,…

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Q: Let (a, b) = 1. Prove (a2, b2) = 1.

A: Let (a, b) = 1. Prove (a2, b2) = 1. Given (a , b) = 1. Which means a is relatively prime to b

Q: Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can…

A: We will use standard division algorithms to deduce the given statement.

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. Let A = {n? +n € Z:n e Z} and B = {r e Z : r³ – 3x³ + 2x = %3D O mod 5}. Prove or disprove: A C…

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Q: , the cdf is None of the above is correct O 1 4x^2

A: We have given that  f(x) = 8x,        0&lt;x&lt;0.5

Q: Assume that 12 + 22 + · · · + n2 = an3 + bn2 +en + d. Find a, b, c, and d.

A:

Q: Give a formal proof of (4→ B) → [(¬A → B) →B -> В

A: Given two statements A and B To prove that A→B→¬A→B→B Let us construct the truth tables of A→B, ¬A→B…

Q: If o? = 625, X = 66.3, and Zo.025 = 1.96, %3D %3D %3D then the size n is O 10. None of all. 20. O…

A: None of all

Q: If P, stands for "P., then prove that I+1. P, +2. P, +3. P, +...+n. P, = (n+1)!.

A: that is will be...equal the 1 + 1. 1P1 + 2. 2P2 + 3. 3P3 + …. n. nPn = n+1Pn+1. and we know that nPr…

Q: Give a direct proof of the claim: V n E N, Vk E N, if the last k digits ofn are divisible by 2k then…

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Q: 3 Let A = 4 1 Write 5A. Is det 5A = 5 det A?

A:

Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 +n², express an in terms of n.

A: a1=3, a2=4 n≥3; an=2an-1+an-2+n2 First from the given, the given values shows that the terms are in…

Q: (b) {an}, where an 1 if n is odd and an = ; if n is even. |

A: Given that an where an=1n if n is odd and an=n2 if n is even.

Q: Suppose 671 + 3v2 – 203 = 0. - Let w = 301 – 6v2 – 403. Which of the following must be true?

A:

Q: Given that P= (ad), 428 Engineering Mathematics where a +d=-1 and ad-be = 1, show that and hence…

A: Given Problem:- p=abcd Given a+d=-1 and ad-bc=1 Show that  p2=d-b-ca Hence deduce that  p2+p+1=0

Q: If a is divisible by b, then bq, for some integer q. a

A: See the detailed solution below.

Q: If a < b, is a? < b?? (Check both positive and negative val- ues for a and b.) If a < b, is a’ < b*?…

A: Inequality: If a&lt;b let us assume a=2, b=3a2=4 , b2=9Here , 2&lt;3 and 4&lt;9But if we take a=-3 ,…

Q: Suppose that In A = 3 , In B = 4 , and In C = 5 . %3D A? Evaluate In ВС

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)

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Q: If P(n) is the statement "n' + n is divisible by 3' Prove that P(3) is true but P(4) is not true.

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Q: Obtain the values of In(/3 – i).

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Q: 45.r > (рли) ~pv~ w rvs S

A: We have to construct a formal proof of the given arguments.

Q: The value of 5149 in U7 is O 5 1 4 O None of the choices Оз

A:

Q: Which of the following are valid witnesses to show that 10n-1 is (n)? O C=1, k=100 O C=10, k=10 O…

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Q: Given: ACEG is a O. L1 =L2 Prove: AB EF = ED EC

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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: An indirect proof is to be used to prove the following: If AB = AC, then AABD = AACD. Which one of…

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Q: Let A = {r € Z:I mod 7 = 2} and let B = {r € Z: 7|(x – 2)}. Show that A = B. %3D

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Q: elsewhere. ind (a) K (b) CDF of X

A: