Question

S = {xlx is a multiple of 4 and 9

Which set is equivalent to S?
A. {8, 12, 16, 20, ...}
B. {8, 12, 16, ... ,36}
C. {9, 12, 16, ..., 37}
D. {12, 16, 20, 24, ...}
E. {12, 16, 20, ... ,36}

Answer 1

None of the provided options are equivalent to set S, which represents multiples of 36. A correct representation would be {36, 72, 108, ...}.

Step-by-step explanation:

The set S is defined as all numbers that are multiples of both 4 and 9. The least common multiple (LCM) of 4 and 9 is 36. Therefore, for a set to be equivalent to S, it should contain multiples of 36, such as 36, 72, 108, and so on. Looking at the options provided:

• Option A contains multiples of 4 but not all multiples of 9.
• Option B contains numbers that are not multiples of 36.
• Option C has numbers that aren't multiples of 4 or 9.
• Option D contains multiples of 4, but not all multiples of 9.
• Option E has numbers that are multiples of 4, 9, and 36 up to 36, but not beyond.

None of the provided options perfectly match set S because they don't contain the continuous series of multiples of 36. Hence, a correct representation of set S would be {36, 72, 108, ...}.