Problem 1
U = {2,3,8} is the entire universe. It's all of the numbers that exist in this framework. We ignore anything else.
A = {2,3,8} simply copies the universe and lists all the values we care about.
The complement of set A is any number not in set A. But because set A lists everything we care about, there's nothing left.
Therefore, the complementary set is empty.
We can write the empty set as { } which is a pair of curly braces with nothing between them. Not even 0 is part of this set.
Answer: Empty set
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Problem 2
U = {whole numbers} = {0,1,2,3,4,...}
This time the universal set is a bit more interesting, or at the very least, it's much bigger.
Set A is the set of odd whole numbers, so A = {1,3,5,7,9,...}. Notice how anything inside set A is also in set U. We can say set A is a subset of set U.
The complement of set A would be the set of even whole numbers {0,2,4,6,...}. This is the list of stuff not found in set A, but it's in the universal set.
Combing the evens and odds together will help form the set of all whole numbers.
Answer: {0, 2, 4, 6, ...} which is the set of even whole numbers.
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Problem 3
set of whole numbers = {0,1,2,3,4,...}
Because h is a whole number, this means h must be selected from that set of values above and nowhere else.
We're then told that h < -2, but there is no such whole number that fits the description. Something like 4 < -2 is false. If we wanted negative values like this, then we'd have to expand to the set of integers.
Therefore, the set being described has nothing in it.
Answer: Empty set
