Question

Consider the universal set U of all the integers from 2 to 20, including both 2 and 20. Let B be the set of multiples of 2, not counting 2 itself. Find Bc. Write your answer in standard set notation, for example 1,2,3,4,5. Do not use the notation B^c= in the answer.

Answer 1

The complement of set B, which includes multiples of 2 within the range from 2 to 20 except the number 2 itself, is {2, 3, 5, 7, 9, 11, 13, 15, 17, 19}, which comprises all odd numbers in that range plus the number 2.

Step-by-step explanation:

The question asks us to identify the complement of the set B, which consists of multiples of 2 within the universal set U, where U contains all integers from 2 to 20. The complement of B, represented as Bc, includes all elements that are in U but not in B. Since B includes all multiples of 2 (from 4 to 20), Bc will contain all odd numbers from 3 to 19 and the number 2 since 2 is explicitly excluded from B. Thus, we can write the set Bc as {2, 3, 5, 7, 9, 11, 13, 15, 17, 19}. Note that 1 is not included since it falls outside the range defined by U.