7. Let A and B be bounded nonempty subsets of R, and let A + B := {a+b : a € A, b € B}. Prove that sup(A + B) = sup A + sup B and inf(A + B) = inf A +inf B.

Q: Suppose that A₁, ..., An are bounded subsets of R. Prove that A₁ U… U An is bounded and that sup(A₁…

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Q: Let A and B be bounded NON empty sets of R, and let A + B := { a+b: at A, bt B3. Prove that supla…

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A: (d) Let, x ∈ (A')'       => x ∉ A'       => x ∈ A      So, (A')' ⊆ A. . . . . . (I)…

Q: Use the element method and contradiction to prove that for all sets S and T S Ռ ( T - S) = {  }

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Q: Suppose that A and B are subsets of R which are nonempty and bounded above, and suppose that BCA.…

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Q: Suppose that A and B are bounded, nonempty subsets of R. Prove that AU B is bounded and that sup(AU…

A: Consider the provided question, Suppose A and B are bounded, nonempty subsets of R.

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Q: Suppose F and G are families of sets. Prove that (UF)n (UG) ≤ U(F N G) iff VA EFVBE G(An BCU (FNG)).

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Q: = (4) Suppose that A is nonempty set that is bounded from above and let B Prove that B is bounded…

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Q: Prove that a set T1 is denumerable if and only if there is a bijection from T1 onto a denumerableset…

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Q: Let ACR be a nonempty bounded set. Prove that sup A is unique.

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Q: Give an example of a closed subset S of R2 such that conv S is not closed.

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Q: Let A, B be bounded subsets of R. Let A+B = {r+y:1 € A, y E B} and AB = {ry : 1 € A, y € B}. Which…

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Q: Give a counterexample to show that the statement For all sets A, B and C, if A⊈BandB⊈C,thenA⊈C.…

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Q: Exercise 1.2.10: Let A and B be two nonempty bounded sets of nonnegative real numbers. Define the…

A: We have  Let A and B be two nonempty bounded sets of nonnegative real numbers. Define the set C: {ab…

Q: Let A and B be subsets of U, n(U)=90, n(A’∩B’)=20, and n(A–B)=n(B–A)=30. Determinen(A∩B).

A: It is given that A and B be subsets of U.