Which of the following statements are true or false? Give reasons for your answers in the form of a short proof or counter-example, whichever is appropriate:

i) Every infinite set is an open set.

ii) The negation of p∧ ~ q is p → q.

iii) −1is a limit point of the interval ]−2 ,1],

iv) The necessary condition for a function to be integrable is that it is continuous.

v) The function  defined by   is differentiable at 

i) Every infinite set is an open set.
False. A counterexample is the set of all real numbers ℝ, which is infinite but not open. An open set is a set in which every point has a neighborhood contained entirely within the set. However, in the case of ℝ, it includes its boundary points, so it's not open.

ii) The negation of p ∧ ¬q is p → q.
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