= {1,2,3}. 2. Prove that A = B where A = {x € N: (n − 3) (n + 5) ≤ 2n} and B = Hint: You need to prove both ACB AND BCA.

Q: Let = n n i=1 x₁ . Then for constants a and b, n Σ a(x₁ - ī) b² =? (6²5m)

A: The question is about parametric inference.Given :Where,X1, X2, ...., Xn are independent random…

Q: Find 3 values of r n =120 o(n) such that

A: Ok

Q: Show that if x > 9, then x³ – 8x? + 2x > 3. Show that for all n e N, if n > 10, then nª – 2n² > 3n³.

A:

Q: 6. Let An = [−3⁄, 1 + ¹). Find ♂ Añ and justify (not prove) that your answer is correct. n=1

A:

Q: . Show that p(X) = XP-1 +... +X +1 when p is prime.

A: For every integer n≥1, the nth cyclotomic polynomial Φn is the monic polynomial whose complex roots…

Q: Determine inf H and sup H for H = (-1, 0), H = {0, 1}U(2, 3),

A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: X1 Xi + 2x3 , X1, X2, x3 ER – 4.x2 T: R³ → R², T x2 X3 - x3 ||

A: So first we prove that the given transformation is linear

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A: I have disproved the result

Q: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: Let A = {m CZ/m = 4k+8} where k CZ, and let B = {n CZ/n=2r + 2} where r CZ. Show |A| = |B

A:

Q: Let a = i +43 + 2k. Find ||a||. −

A: Given, a→=-i→+4j→+2k→

Q: is a1 = 2, a2 =3, and an  = 5an–1 – 4an–2 for n > 2 expressed in explicit formula? true or false?

A:

Q: (4b) Let n E Z. Prove that if n is even, then n² + n + 2 is even.

A: