Discussion
Let A ={ x: x is a positive multiple of 2 less than 36}, B ={ x: x is a positive multiple of 3 greater than 16}, and c ={ x: x is a positive multiple of 4 less than 42},. Then (A ∩ B) ∩ C=
Answer: C
The intersection is {24}.
List the sets. A holds the positive even numbers below 36: 2, 4, ..., 34. B holds the multiples of 3 above 16: 18, 21, 24, 27, 30, 33, 36, ... C holds the multiples of 4 below 42: 4, 8, ..., 40.
\(A \cap B\) keeps the even multiples of 3 between 16 and 36, that is the multiples of 6: {18, 24, 30} (36 is not in A, which stops below 36). Of these only 24 is a multiple of 4, so \((A \cap B) \cap C = \{24\}\).
{12, 24} and {12, 24, 36} include 12, which is not greater than 16, and 36 is excluded from A, so {24, 36} fails too. The intersection is not empty, so φ is wrong.
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