Example:

• E = { x: x = 2n for n N }
• O = {x : x = 2n + 1 for n N }
• I = {x R: x * x = -2}

Find the sets O E, O I, comp(I).

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• O E is the set of all natural numbers that are even or odd. Hence O E = N.

• O E is the set of all natural numbers that are both even and odd. Hence O E = 0 (empty set)

• comp(I) is the set of all numbers that are not in I. Since I is empty, it is the set of numbers that are not in the empty set. Hence: comp(I) = R (here again the universe is understood to be all real numbers).

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(bgw)