Question

Let U=[1,23,...,16] C=[1,3,5,...,15] Use the roster method to write the set C'.

Answer 1

The complement C' of some set C is essentially the set we get when we remove all of the elements of C from the universal set U.

Here, our universal set contains all of the numbers 1-16, and the set C contains all of the odd numbers between 1 and 16. If we were to put both of these sets in roster form:

$U=\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16\}\\C=\{1,3,5,7,9,11,13,15\}$

If we remove all of the elements of C from the universal set U, we're left with the complement of C, which contains all of the even numbers between 1 and 16:

$C'=\{2,4,6,8,10,12,14,16\}$