= {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: 2. (3+j4)(6+)7) convert to polar form (Az0) Hint: x = en(x)

A:

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: 3xt lim x0 5x4 +3x3 + 9x3 is А. 6 B. does not exist С. 2 D. 3

A: Given, limx→03x4+9x35x4+3x3

Q: Use membership tables to prove that A – (Bn C) = (A – B) U (A – C). %3D |

A: We want to prove the set identity A-(B∩C)=(A-B)∪(A-C) using membership table . Here we will use…

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: Prove that : L²₁ (1-x²) Pm Phd x T 0. 2n (n + 1) 2n + 1 4 mn. m = 11. m, ne N

A:

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: 2F. n 1 ;;1=2" (b), (26)

A:

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

Q: Please

A: We know that, Statement: If P then Q. Contrapositive: If ~Q then ~P.

Q: For all n, d EZ where d + 0, d\n n = dk for some kEZ. Disprove: For all integers a, 6, and c, if…

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: -1 1 Let A= 1 Then, ||A||2 = -2 Select one: a. 9+V45 2 b. 8+V45 c. 10+V45 2 d. 7+V45

A:

Q: Let a = i +43 + 2k. Find ||a||. −

A: Given, a→=-i→+4j→+2k→

Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

A:

Q: 5. For n ≥ 1, establish the formula (2n + 1)² = (4tn + 1)² – (4tn)².

A:

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

A:

Q: 16. Assume that a < 0 < b. Use a geometric argument to show that b - [²x dx = 5² = ² 2 a

A: Using geometric argument we have to show that ∫abx dx=b2-a22, where a&lt;0&lt;b.

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

A:

Q: Q5: Suppose B is real. Show that le2ßt - 1|< 27|B| , 2 πβί

A:

Q: 2x P(A) i. For what values of x are A and B mutually exclusive? For this value of x, are 5. Suppose…

A: Basic probability

Q: Suppose b1 + *+ bm < n. Prove that b,!bm!< n!.

A:

Q: (b) If r23= 1, prove that R² (23) = 112=113 and 01.23 = 01 (1-12).

A: