3 *|. Then Let A O a. ||A||1 = 0 O b. ||A||1 = 2 || 4||1 = -3 O d. ||A||1 = -1 O c. O e. ||A||1 = 7 O f. ||A||1 = 5 O g. ||A||1 4||1 = 1 O h. ||A||1 = 4 O i. ||A||1 = 3 O j. ||4||1 = /27

Q: 3) Prove that ae*+be-x a) b b > 0 ex+e~x

A:

Q: if A) B) none of these a(n) a(n) is smaller or equal to oo then is finite

A: In the question we have to select correct option.

Q: 4. Let IR be the set of all real numbers, xER and n EN such that n 2 2. If (1+x)> 0, prove that Pn :…

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A:

Q: а - 2b Assume that S = then dim (S)= a a,b eR b O 2 O 3

A:

Q: can you solve it urgently ?

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A:

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A:

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A: Introduction: When we add the terms of an infinite sequence, it becomes an infinite series. Likewise…

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A: The solution is given as

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

Q: assume that Pr[A]=0.25Pr[A]=0.25, Pr[B]=0.35Pr[B]=0.35, and Pr[A∩B]=0.1Pr[A∩B]=0.1. 1)Pr[A|B] =…

A: Given: P(A) =0.25 P(B)=0.35 P(A∩B) =0.1

Q: 2. A find det A, ad) A N ト

A:

Q: Let a, b eR with a < b. Assume that a + <b - for all n E N. Show that b- = (a, b). %3D n n=1

A: We will show  two sets are equal.

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A:

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

A: Where a, b&gt;0

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A:

Q: (a) For all a, b E R, if a E Q \ {0} and b & Q then ; ¢ Q. (b) For all x, Y E R, if x is irrational…

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A: We have to solve given problem:

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Q: - such that n >r > 1, (n – 1)! r!(n – 1 – r) n! r!(n – r)! n - r -

A:

Q: Show that 1-r for any r 1 1 and any 3. nEN

A: answer

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A: Use the infinite sum of geometric series. S = a/(1-r) Where a = first term              r = common…

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A: "By Bartleby rules, only first three sub-parts of question 1 have been answered"

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A: We have given that  Standard normal i.e, Z~N(0, 1).

Q: 4. Let R be the set of all real numbers, xER and n EN such that n 2 2. If (1+x) > 0, prove that Pn:…

A: Let ℝ be the set of real numbers, x∈ℝ and n∈ℕ such that n≥2. If 1+x&gt;0, we want to prove that  Pn…

Q: Given x > 0 and a real number y, there is an n in N such that nx > y.

A:

Q: Show that E-o (-1)*(")=0, and then verify that () + C) + C)+ - = (") +C) + () +-- -G) + G) + G)-…

A: We can show given identity by definition of Binomial theorem:

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A:

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…

A:

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: Prove the following statements: i. Let x, y and z be integers. If exactly one of x,y and z is odd…

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A:

Q: 2. Prove that any two non-zero elements a, b in a P.I.D. R have a g.c.d. Further if d e R is a…

A:

Q: 4. Let R be the set of all real numbers, xER and n E N such that n 2 2. If (1+x) > 0, prove that P,…

A:

Q: Let...

A: Given expansion formula is  a+bn=∑nkk=0nan-kbk

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A:

Q: Let a, b e R with a < b. Assume that a + <b - for all n E N. Show that 1 = (a, b). a + ,b n n=1

A:

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A: 3) to evaluate

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A: This is a problem of the recurrence relation.

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A: Option (c) is correct.

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A: We need to see if the converse of the statement "gcdn,m=g then there are a,b∈Z with an+bm=g" is true…

Q: Given p(x) = x + 4x²-3x+2 and =x +5x +2 R4. P(x) X-1 Which statement is true? Select all that apply.…

A: Topic:- algebra