Prove that the set {x ∈ R | x + x 2 < 0} is bounded above.   Give an example which demonstrates that the statement “A is bounded below if and only if Ac is unbounded above” is false. Explain your example in detail. Recall that Ac is called the the complement of A and is defined to be Ac = {x ∈ R | x 6∈ A}

Please mark all true statements (there might be more than one statement that is true). Let A CR be finite then A is an open subset of R. ○ The set A = {x² + 2x + 1: x € R} is an open subset of R. Let A CR be infinite then A is an open subset of R. t D ( x₁₁² ) = {x € R: Intersection of open sets open. Let D(x x € R: x-x| 0, such that tD (x₂ε) ≤A. 0

Exercise 3.3.15. Prove or find a counterexample to the following statement. Let A, B and C be sets. Then (A-B) UC = (AUBUC) - (ANB).