Prove that if f: A → B is a 1-1 function and B is countable, then A is countable.

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A: Approach to solving the question: Detailed explanation: Examples: Key references:

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A: Step 1: Step 2: Step 3: Step 4:

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A: Step 1: Step 2: Step 3: Step 4:

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Q: Q2/Determine: 1. L-1 s²+9s+2 2. L-1 L(s+3)(s-1)2. s+1 (s-1)s²]

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Q: please answer correctly.

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Q: what is the last digit of 2^123 + 3^45? (hint: find the pattern for each number separately before…

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Q: 3 0 0 Find the characteristic polynomial f(x) of 28 -5 f(x)= = - -16 2 1

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Q: need help

A: Step 1:a) Number of ways to choose a group of nine :17C9​=9!×8!17!​         =24,310 Step 2:b) i)…

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A: Flux can be calculated by using the formula Flux=∫s​F.ndS.Here, F(x,y,z)=(y−x,y+x,1)Now, Surface S,…

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Q: find the eigenvalues of each matrix and determine a basis for each eigenspace. -3 -12 0 0 30 -4 -8

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Q: HHHHHHAJHASJHKSHAKSHASHAHKSHKAHSJKAHSKJAHsaldaslhdfasl please helep i want an expert

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Q: refer  to  image  below.  It  has  both  parts  of  same  question.

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Q: Fixed Cost (FC) per month Variable Cost (VC) per unit Selling Price (S) Break-even Volume (x) Total…

A: a. break even volume = fixed cost/(selling price-variable cost)=8,800/(37-23)=628.57 or 629Total…

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Q: Solve the differential equation บ'' "-y-12y=-4-5₁(t), y(0) = −2, y'(0) = 1 using Laplace transforms.…

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Q: 3.- Check the veracity of the following identities: sec(0) - cos(0) 1 + sin(0), = tan 0

A: Solution-

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Q: 8. Solve the following simultaneous equations: In x + 2 lny = In 3 (1) In x + Iny = 1. (2) [Hint:…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: 1. In this exercise we will prove that Z[√-5] is an integral domain but not a unique factorisation…

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Q: 2. Matrix A below is a singular matrix, calculate the value(s) of q. A = [3 2²²q] 32- [5 marks]

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Q: Calculate the value of rhe following limits

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Q: Consider the first-order differential equation given by: dy + p(t)y = g(t)y". dt (a) This equation…

A: Step 1: Step 2: Step 3: Step 4:

Q: please answer correctly

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Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: Approach to solving the question: Detailed explanation: Examples: Key references: Therefore the…

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A: Step 1: Step 2: Step 3: Step 4: