1.7. Problem 7. Part 1. Suppose A1,..., A, are sets and each fi : A → Ai+1 is surjective. Prove or disprove: fn-10 fn-2o f2 o fi : A1 A, is surjective. Part 2. Suppose f : N → A is surjective. Prove or disprove: A has the same cardinality as N.

Q: QUESTION 14 Consider the following statements: T(x, y): "x eats y". A(x): "x is wise". S(x): "x is…

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Q: What is the cardinality of the set of 2 x 2 matrices over N? Prove your answer.  Note: a 2 x 2…

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Q: 5. Prove that S(n +1, k+1) = £ $(m, k) (").

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A: The above inequality is an application of Markov-Chebyshev inequality.

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A: G(x)=1f-1(x)f(3)=2 , f'(3)=1/9

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A: As per our guidelines we are supposed to answer only first one. kindly reposed other part in the…

Q: Show that the series 3. + + 4 To t (-1) Lonverges absolutely.

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Q: 20-22. Your friend claims that AJKL - AMNO by the SAS Similarity Theorem. Here are the information…

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Q: 2. By replacing f in Problem 1 with certain well-known multiplicative functions prove (a) E \u(d)| =…

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Q: 5. Consider the functions l : N → Z by if n is even l(n): 1- n if n is odd 2 Is l one-to-one? onto?…

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Q: Suppose that {$1,...Øn} F p and I F ø; for all i < n. Show that I F þ.

A: Proof: Suppose ϕ∈Γ∗ϕ∈Γ∗. As Γ∗Γ∗ is maximally consistent it clearly follows that there exists a…

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Q: b) If d = 1, prove that (1 if a is odd gcd(a, 2b) %3D if a is even

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Q: 1] Let X,YER. Prove that VxVy(4x+9y>9⇒(x>5/4 Vy> 4/9)) using method of indirect proof.

A: Prove that ∀x∀y4x+9y&gt;9⇒x&gt;54∨y&gt;49, where x, y∈ℝ. Prove the statement using method of…

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A: The objective is to find Z_2×Z_2.

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

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Q: 12. Start with the identities x2 1 P, (x) = xPn-1(x) + *P(x) n P, (x) = xP-1(x) + nP,-1(x ) (a) Show…

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A: Let n≥3. Let σ∈Sn such that σγ=γσ for all γ∈Sn. Suppose σ≠i, the identity Then there exists…

Q: 2. Compute the convolution of the following signals for n 20 n n x1(n) = and x2 (n) = (;)" u(n) n…

A: Consider the expression of . Determine the z-transform of .

Q: Show that 2"=nCk and 0 = [(-1)^nck k=0 HINT: Consider(1-1)" and (1+1)" k=0

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Q: Show that the Post Correspondence Problem is decidable over the unary alphabet S = {1}.

A: To Prove :- The Post Correspondence Problem is decidable over the unary alphabet S =1.

Q: *prove that for . P+2+3+... +n° = 2 n=!,2,3,

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Q: 3. Show that if A-1 exists, then eAT dr = A-1(eAt – I) = (eAt – I)A-1.

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Q: Now, from the relations in (6) we get Wn = µ+ kn (Wn-1 + Wn-2) and zn = € + Vn (žn-1 + Zn-2). (9)…

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Q: Question 13 Indicate if the following statement is TRUE or FALSE. Briefly justify your response with…

A: Solution: Given statement is TRUE

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Q: 6.4 # 2 Find the matia * ' elative to the basir B' for T A' =

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Q: Prove that: (1+ x)*** (n+ 1)x C. + + 2 3 n+1

A: I am going to solve the given problem by using some simple calculus to get the required result.

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A: Given the data:

Q: 33. Use the Squeeze Theorem to prove (sinn/n} c) {3"/n!} b) fn/2"} f by contradiction. a)

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Q: Now, from the definition of k(m), given by equation (1.135), we find on setting n = 0, 1, 2, ...,…

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Q: Suppose  there exist transposition f_i , 1<=I<=t  such that

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Q: 3 5 The Wronskian of {X2,x2}

A: The given set is: x32,x52

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Q: 6. If X has full rank, so that P = X(X'X)-1X', prove that C(P) = C(X).

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A: Consider the provided question, Define f:C→0,12 by f03.d1d2...=02.d12d22...,02.d12d22... We have to…

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Q: 4) Let m,n, r E Z with m # 0 + n. Show that gcd(m, n) divides r if and only if there exist a, b E Z…

A: Let gcd(m,n) divides r. Then we have to prove that, a·m+b·n=r Since, gcd(m,n) divides r than by…

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Q: In Z, let H = &lt;5&gt; and K = &lt;7&gt;. Prove that Z = HK. Does Z = H X K?

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Q: If X(z) = In(z - 2), then what's x(k O a. -ak O b. ak O c. -ak /k O d. others Oe. ak / k O O

A: Given that X(z) = ln(z - 2) We have to find the value of X(k).

Q: 7) Show that K± = det [ T 4 J.

A: Sol