For each of the values on n and d given, find integers q and r such that n = dq + r and 0 is less than or equal to r and less than d: n = 3, d = 11

Q: Define sets A and B as follows  A = { n E Z | n = 6r+4 for some integer r and B = { m E Z| m = 18s…

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Q: If h(t) t" where n is a natural number, then what is h'(t)?

A: If h(t)=tn, where n is a natural number then our aim is to tell the valueof h'(t)=?

Q: * For each integer n, let Cn = {n²,n³, nª}. How many elements are in each of C-2, C-1, Co, and C3?…

A: The set always contains the distinct elements. Given Cn = n2 , n3 , n4 Consider C-2 = (-2)2 , (-2)3…

Q: Prove by direct proof that any integer n ≥ 3 can be part of a Déjà vu Pair n = [11 · · · 1]b for…

A: Given: Any integer n≥3 can be part of a Déjà vu Pair n=11...1b for some base b≥2.   To prove: The…

Q: For any n e N, let An = {x € R | –n <x < n}. Prove that NneN An = A1. (Recall that we define 0 ¢ N.)

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Q: Prove the following: If ā and b are in R', then (5 -a)×(5 +a)=-2(āxb).

A: Given a⇀ and b⇀ are in R3. To prove :  b⇀-a⇀×b⇀+a⇀=-2a⇀×b⇀

Q: Given that S = {x|x €NAr < 20} and A, B, C C S with {r |3|r} {r|x | 560} {x|gcd(r, 110) = 1} A where…

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Q: Given n=35. x=13. Find out the value of y=? (all possible) such that (x*y) mod 35=1.?

A: We will use (13y)mod35=1 to find all possible values of y by writing given congruence in expanded…

Q: If A = (; A-: )-..R. e M2x 2(R), find A" for any positive integer n.

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Q: For each n e N, let A, = (}, } + ) %3D Find Unen An. Find Nnen An.

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Q: An open-topped box is constructed froma square piece of cardboard by removing a square of size 5…

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Q: Show via proof that for two positive integers a, b where a 2 b, (use combinations e.g. n choose k)…

A: We shall prove for the given statement. Though it has little ambiguities.

Q: For each integer n, let T, = {n, nº}. How many elements are in each of T2, T–3, Tị, and To? Justify…

A: To find:The elements in T2, T-3, T1 and T0.

Q: Find the largest number d such that if |x – 3| < 8, then |5x – 15| < ɛ, where ɛ = 1 Repeat and…

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Q: Suppose that S and T are points on the number line , ST = 17 and S lies at 4, where could be located…

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Q: Suppose that E and F are points on the number line . If EF = 11 and E lies at 3, where could F be…

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Q: Given that Z - N (0,1), find k if P(\Z| < k) = 0.8. %3D O 1.282 O -0.253 O 0.842 O -4.5

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

Q: Suppose: n ≥ 3 and x,y ∈ Rn , |x - y| = d > 0 and r is some +R, Need to show: 2r = d, there is…

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Q: that Edn H(n/d)7(d) = 1 and Edn H(n/d)o(d) = n for all n, where r(n) = d(n) and σ(n) = σι (n) Σm d.…

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Q: Let S be a set of integers defined as follows:   2 ∈ S if n ∈ S, then n2 ∈ S if n ∈ S, then 16n…

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Q: Let a and b be natural numbers and define d = gcd(a, b). Prove that alb iff d = a. For all sets A,…

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Q: Define sets A and B as follows: A = {n €Z|n= 8r - 3 for some integer r} and B = {m €Z|m = 4s + 1 for…

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Q: 4. Let E CRd, and for each nE N, define On as the set On z d(x, E) 1/n) Recall that d(x, E) inf{| -…

A: To prove the openness of the given sequence of sets

Q: Let A and B be the following sets: A = {m ∈ Z | m = a^2 +3 for some odd integer a}, B = {n ∈ Z | n…

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Q: ssnip

A: Given: B=abcd A=1234 AB=BA AB=1234abcd     =1×a+c×21×b+2×d3×a+4×c3×b+4×d     =a+2cb+2d3a+4c3b+4d

Q: The ancient Greeks had the following definition: two lengths (positive numbers) a,b are com-…

A: (a) The negation of Pythagoras’ claim can be stated in simple terms as, “there exist at least one…

Q: Define sets A and B as: : {n E Z\n = 4r + 3 for some integer r}. • B= {m E Z m = 4s – 1 for some…

A: the objective is to solve the above questions.

Q: Let 2= R, and suppose S₁ consists of intervals including Ø, the empty Ω set: S₁ = {(a,b]: -∞ <a ≤ b…

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Q: 'ind integers s and t such that s · 35 +t · 78 = 1. Show your work.

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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: For m,n E Zt, define P(m, n) to be: (п + т - 1)! n!(m – 1)! the number of ways to write n = x1+ ·…

A: As per our guidelines, we are supposed to answer only one question(3 subparts) and rest can…

Q: Tind the values of X, and X, and find such that possitive number f -11<0.1 whenever O<|x-< 6

A: We are given a graph of the equation y=1x and asked to find the values of x1 and x2 for which its…

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: For each integer n > 2, let P(n) bè thế för n-1 Eili +2) = n(n-1)(2n + 5) 6. %3D i=1

A: Given                   P(n):   ∑i=1n-1i(i+2)=nn-12n+56,          n≥2

Q: Let the numbers c1, C2, ... be defined inductively as follows: c1 = 0 and for every n >1 the number…

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Q: Let M=( 3 Find formulas for the entries of M", where n is a positive integer. Mn = =

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Q: Find the total number of in H.C.F. of n and 36 is 1.

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Q: "for all n,m ∈Z \ {0},  gcd (n,m)= 1 then there are a,b ∈ Z with an+bm= 1" is the converse of the…

A: It is given that if,  gcdn,m=1 then there exists a,b∈Z such that an+bm=1 To show that converse of…

Q: For each integer n, let Tn = {n, n2}. How many elements are in each of T2, T3,and T1? Justify your…

A: Given that, Tn=n,n2. Substitute n=2 in Tn=n,n2  to find the number of elements in T2. T2=2,22=2,4…

Q: -) If A and Bare 3 x 3 such that det A = 3 and det B = 2 } Find, if possible, the value of det(A²…

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Q: b. H = {x E G|x" = e} for a fixed positive integer n.

A: Given set in part B

Q: for each positive integer i. Find each of the following. (Enter your answers using interval…

A: Since you have posted multipart question and i can answer three subparts at a time. So answering…

Q: Find B and A such that o(x) is continous: o(x)= {13-Bx.     x<-5}           {3x^2 -1.   -5 less…

A: The given piecewise function is: ox=13-Bx      for  x&lt;-53x2-1        for   -5≤x&lt;42x+A…

Q: Define sets A and B as follows: A = {n € Z ]n = 6r + 4 for some integer r} and B = {m € Z [m = 18s-2…

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Q: For each integer n, let Tn = {n,n²}. How many elements are in each of T2, T–3,T1 and To? %3D Select…

A: Given that for n∈ℕ, Tn=n,n2. Thus number of element in,  1.  T2=2,22T2=2,4 2. T-3=-3,-32T-3=-3,9

Q: For each of the following pairs of numbers (a, b), find ged(a, b) and find integers s and t such…

A: Part a )- Given : Given pairs of the Numbers are 25,30 Calculation: First we find gcd25,30 Therefore…

Q: (a) For integers a, b, q, r, prove that if a = bq + r then (a, b) = (b, r).

A: Since you have posted a multiple question according to guildlines I will solve first(a)    question…

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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Statements and Logic

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