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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: Vhich of the following are correct?

A:

Q: 1. Give a proof of the following statement. 3 integer c > 0 V integers r > 0 3 integer d > 0 : x² –…

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

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Q: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

A:

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: 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: What are the values for x1, x2 and x3? O x1-500 ; x2-57.78, x3-175.56 O x1-500; x2=-175.56, x3-57.78…

A: We have given optimization table and we have to find the values of variables that maximize the…

Q: 2. Prove: A – B = ANB

A:

Q: P. IN 0 -24 -20 5 2=1,4 1. -1 9 - - 1 O A. For P = 10 4 Click to select and enter your answer(s) and…

A: The required P matrix has been obtained from digonilization of given matrix in step 2 and step 3.

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

A: Similar triangles

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

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Q: 9. Give a proof by contradiction to show if A and B are sets, then A N (BN A') = {}.

A: Suppose A and B are sets.

Q: Show that /2, /3, 5 cannot be the terms of a single A.P.

A:

Q: Which of the following is not equivalent to 23 + (-27) - 16- (-32)? O 23 - 27- 16 - (- 32) O23- 27…

A: 23 + -27 - 16 - -32Total ⇒ 12Result: Option IVth• 23 + -27 + 16 + 32   Is gives total = 24   So 12 ≠…

Q: Prove by contrapositive: If a+b is odd, then a is odd or b is odd.

A:

Q: 2.1. Prove that B Is erse of A -17 11] -7,B: 0 3 2 [1 1 2 2 4 -3 [3 6 -5] 2 A = -1 11

A: To prove that B is the inverse of A.

Q: 7. Prove: Vn,meZ, if n and m are odd, then n·m is odd.

A:

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

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Q: -107 8- 6+ E 4+ 10--8-6 -4-2 2-4-6-8-10- IS RA

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Q: АР 10. In AABC, PB PQ and QC 1 If PQ = v and QB = w, express the following in terms 3 1 of v and w:…

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

Q: A = 13 ;Prove A2 - 5A = 21

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Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

Q: O 1srs2 Osrs3 Non of these Osrs2 144 7 8 U K S 10

A: We know : x=r.cosθ  and  y=r.sinθ Therefore, z=x2+y2=r.

Q: If {e: 3 is an H₂ then Брасе either empty bits ar O Y loo

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Q: I. List all postulates of EG

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Q: jP a € Z then 24 4 is not afactor of 3 + |

A:

Q: = [; 4 3 Then, A is not SDD. Let A -1 1 Select one: True False

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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<x<0.5

Q: 23. Suppose P(A) = .40 and P(B\A) = .3O. What is the ioint probahilitu of A and B? %3D

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Q: 5. Write a proof. Given: ZE = ZH ZHFG = ZEGF Prove: AEGF= AHFG G

A: We will prove the following.

Q: 2. Use a proof by contrapositive to show the following: Suppose a, b e Z are integers. If a² (b² –…

A: To Proof- Use a proof by contrapositive to show the following: Suppose a, b ∈ ℤ are integers. If…

Q: 5. If A = I then what is A?

A: Here given as A2=I Taking determinant both side A2=IA2=1A=±1 Thus A is non singular and inverse of A…

Q: 4. Prove or provide a counter example for the following: (AU B)nC = (AnC)U(BnC)

A: We need to prove that(A∪B)∩C=(A∩C)∪(B∩C)If we have to prove that(AUB)∩ C C C…

Q: Show that 1 Is En=1 2 1?+ 1 4

A: (Solving the first question as per our guidelines) Solution: The series is ∑n=1∞1n2+1 Split the…

Q: II. Prove the following. 3. 7|23n – 1, Vn EN -

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Q: 3. Evaluate ". a, Inutc b. In u C. Inx+c

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Q: 45, n-1 on? 12 1 2, ns 1, Al 7(n 11, what is the

A: This is a problem of inhomogeneous recurrence relation and counting.

Q: 18 odd- 2. PAMO We mus t sholw there 18 an Af pd and Cat Calt 2) 2 To even evea 12

A: The objective is to show that, if n(n+1)2 is odd then (n+1)(n+2)2 is odd. Take the negation of the…

Q: a If 2" = ア,what is

A: Taking log both sides of the given equation

Q: 6. No : o Show that sa= (Q-1)a

A: To show :- ∆ ax = a-1 ax

Q: 9) Determine whether AMNO = AQRS. Explain. M(0,-1), N(-1,-4), 0(-4,-3), Q(3,-3), R(4,-4), S(3,3)

A: Given, M0,-1;    N-1, 4;    O-4, 3Q3, -3;    R4, -4;   S3, 3 We have to determine whether  ∆MNO…

Q: 1. 1. Is it true or false? A - |4| Birini seçin: O Doğru OYanlış

A:

Q: II. Prove/Disprove: 1. (¬A → ¬B) Ð (¬C ^ A) = ¬(A v ¬B) →¬(B –→ C)

A: Solve the Expression using boolean algebra   ¬a⇒¬b=a∨¬b(a∧¬c)⊕(¬a⇒¬b)=(a∧c)∨(¬a∧¬b) Also, the…

Q: (b) Give the contrapositive of the following statement concerning positive integers n,a and b: If n…

A: The negation of [a≤√n or b≤√n] is : a > √n and b > √n And, the negation of, n = ab is, n ≠ ab…

Q: What is the converse of "If there is ice on the lake, then it is cold?"" If there is not ice on the…

A: converse of "If there is ice on the lake, then it is cold" is ? Converse means q-->p

Q: Which of the following is the contrapositive of the sentence " If n2+4n+5 is odd, then n is even"?

A:

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

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

Q: What conclusion can be drawn from the following? State the property used (transitive, symmetry,…

A: When a set of premises is given, one can draw a conclusion from the premises. Many rules of…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.