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A: Given: F=ℕℕ, R on F×F defined by f,g∈R if fn≤gn for infinitely many n∈ℕ. F=ℕℕ, R on F×F defined by…

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A: Given, the differential equation                  xy''+y'+x2y=0                 ...(1)

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A: The given problem is related with equivalence relation. Given that A = ℤ . Also, given that R is…

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Q: Let S = R^2 2 and define the relation R as follows (x1, y1)R(x2, y2) ⇔ x1^2+y1^2 = x2^2+y2^2 Show…

A: We have to check all condition of equivalent relation  i.e. reflexive , symmetric  and transitive ,…

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A: Given that the size of set A is  8 and size of set B is 4. Now to be total number of functions f:A→B…

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A: I have given the answer in the next step. Hope you understand that

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Q: Chinese Remainder Theorem. Let X, Y be sets and let f: X → Y be a function. We define a relation ~…

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Q: Ex(ia)g prove or dis prove that Ris equivalance relation on x iff Rtis equivalene relakion ony

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Q: 1. Let be a relation on A = {1,2,3,4,5,7,8,9, 11) defined by ay if and only if 2+1 divides y + 1.…

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Q: Let < be a partial order on A. Assume that a,b EA are elements with the property that: for any X EA,…

A: (First part): Reflexive property : Since ≤ is an reflexive relation then for every element x∈A we…

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Q: 38. Let F be a closed set in R. Let y ¢ F. Show that there exists some ɛ > 0 such that the…

A: We have to prove the above statement.

Q: 1 If MR =: 1 lo 1 1., then the relation ol 1 Ris Reflexive Transitive Anti-symmetric Symmetric

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Q: Punctian diffexentiable Af not Is every in tegsable. by then prove it giving countes example.

A: No, every differentiable function is not Integrable. Consider the function f(x)=1x  in (0,1). Obtain…

Q: How many funcei ons F{,2,3,4is}→ {l,2,3} are ehere eien er FCI)=1, F(2) 2, f (3) =3? or

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A: Given: R=x, enx : x∈ℝ, n∈ℤ. To Prove: R is an equivalence relation on the set of real numbers.

Q: っ+8 fen) 21, i) Draiw groph ci) what domain and are lange cii) Dees Limita f) exist, point of…

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A: We can answer all parts as below.

Q: 7. 5 R 3? Is 2 R 8? Is 8 R 2? Define a relation R on Z by x R y if and only if x-y ≤ 3. Is 3 R 5? Is

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Q: List the ordered pairs in the relation R from A=0,1,2,3,4, B= 1,2,3, 4, 5, where Ris defined as (a,…

A: Given sets are: A={0,1,2,3,4} B={1,2,3,4,5} Relation R consist of those ordered pairs (a,b) such…

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