Given this formula 1 ARL, where B = SLCL NC41,dx 1-B

Q: 5. Negate: "There exists a student in this class who is a History major." Your answer should not…

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Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: 1=(3 O Given that A= (i) AB (ii) |B| (iii) AT -2 5 (!) 2 and B = -3 4 0 1 -1 6 2 " determine

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Q: 2 If C = |2 -1 0 Show that (C")-1 = (C-')" -2 2 2

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Q: a. S ((e'+4)²-9)3/2 -dt

A: Given the integral ∫etet+42-932dt . The objective is to find the given integral ∫etet+42-932dt.…

Q: aluate. 11! 4!(11- 4)!

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Q: If P(A) = 0.29 , P(B) = 0.32,  P(A | B) = 0.38 then P(A ∩  B) =

A: Bayes' theorem can be used to compute conditional probabilities and isexpressed as P(A|B)…

Q: Find the L(e2" (1+ t)²). ,2t a) + (s-2)* 1 b) + (s-2)2 2 (s-2)3 (s-2)2 c)+2 (s+2)³ (s-2)? d) +…

A: The following formulas can be used to obtain the Laplace transform.…

Q: (s-4) L-lis2-85-9). Find L-1

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Q: (a) Compute A2, A3, .•. , A7• (b) What is A2015?why?

A: (a) Compute A2, A3, .•. , A7• (b) What is A2015?why?

Q: What is the order of in GL2(R)?

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Q: (1) How much is 0! ? (by convention on). 0!

A: (1) Given

Q: Show that la 1 1 1 a 1 - (а + 3)(а - 1)3. - 1)³. %3D 1 1 a 1 1 1 a

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Q: (2) Ip xyl S1 or Cxy s0,0, Preoue the tollowing propedty

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Q: A= 1 0 0 0 0 -1 7 3 3 1 2 1 لنا Low 0 1 0 21 1 0 5 -6 001 2 B= 3/2 6 1 -1/2 3 5 -2 2 1 -6 - 4 1 1 0…

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Q: . Write (12)(13)(14) in the form æ(12), where a E A¸. Write (1234) (12)(23), in the form a(1234),…

A: Given, (12)(13)(14) and we have to write this in the form alpha(12), where a in A4. Similarly, write…

Q: V ) and A, p 0, and e0. Show that then I',AF0.

A: In the given question  given that γ l=(φ∨ψ) , ∆,φl=θ and and also ψl=θ then we have to prove that…

Q: Prove c (A + B) = cA + cB   (c + d)A = cA + dA   c(dA) = (cd)A  IA= A

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Q: 3. (a) 5e (b) 2e-21

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Q: Show that for any n E N, 7(15".

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Q: This exercise should be done two ways: by hand and using technology where possible. Let A = 0-202 0…

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Q: In S, if T-{(G { G {), them r ) is In S, if T-1(G )G 2 3 \1 2 3 2 3 }, then 3 1 2 3 2 3

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Q: /(r² – 8)5

A: Use substitution method to find the integral

Q: 7. f : N2 → N.

A: (1) N2 ={(m,n): m,n∈N}     This is the sketch of the bijection f:N2 →N The curve which is traced on…

Q: (2,3,1)(1,2,4) e S5.

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Q: Show that (a + b)x = ax + bx for all a, b E F and all x € F¹.

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Q: Show that |Z × Z|=|N|

A: ℤ represents set of integers ℕ represents set of natural numbers  To show ℤ×ℤ=ℕ We know that|ℕ|=α0…

Q: Evaluate foxe*² dx . 2 0 a. b. OC. O d. 9 =/12 + C 2 2 (e⁹-e) + C (e⁹-1) + C (eº-x²) + C

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Q: L[t?e-3t] = ? 3! 3! (s+3)2 (s+3)3 2! 2! (s+3)2 (s+3)3

A: To find- ℒt2e-3t = ?     Formula Used-  ℒtneat = n!s - an+1

Q: L-1 if (24/ ((5-7)²-9) 1 ;)} What's the value of a*c? = atbect senh(3t). =

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Q: If C(12,4)+C(12,5) = C(n, 5), then n is equal to

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Q: Find L-1 [.

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Q: (a) If A₁ = {-i, -(i − 1), . . .−3,−2,−1, 0, 1, 2 }, for i = 1, 2, 3,. . . find (i) Un A6 and (ii)…

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

Q: Compute the following values, showing your work: φ(20), φ(25), φ(54) and φ(8!)

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Q: Show that E(r(r + 1) =- n(n + 1)(n + 2), n E N.

A: We have to show that ∑r=1n(r(r+1))=13n(n+1)(n+2)           ∀n∈ℕ

Q: Find 1 L L 0 0 (3x + 2y) dxdy

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Q: If the numberr of elements h=50 ৭০d । (6) = ५ and 1(5)3D41(h), then the numbor of elements -

A: Answer can be given using the simple concept of  probability.

Q: Show that (m) (2n 4n n

A: As n → ∞, By Striling approximation formula n! tends to  sqrt(2 pie n) (n/e)^n