We have been given a universal set of integers U and a set of natural numbers T defined as follows.
&U={x | x is an integer, x≤ 12 }
&T={x | xis a natural number, x≤ 12}
We can rewrite T in roster form to help us better visualize the elements in this set.
&T={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
We are asked to find T'. In order to do this, let's rewrite the elements of the universal set in roster form too.
&U={..., - 3, - 2, - 1, 0, 1, 2, 3, ... , 10, 11, 12}
Since the complement of a set is the set of all elements in the universal set that are not in the set, we can construct T' as shown below.
&T'={..., - 3, - 2, - 1, 0}
Finally, we can write this in set-builder notation.
&T'={x | x is an integer, x≤ 0}
