
Derek D. answered 07/24/20
Extensive experience in public education, B.A.S in math gr 5-9
Hello Devijn!
First, let's look at the key words in our question, and gather important information and put together what they are asking:
Given that the universal set is all real numbers, write the complement of set A. Set A: {Irrational numbers}
We are told that the universal set, the entire collection, is all real numbers.
We are also told that set A is the set of all Irrational numbers.
What are irrational numbers? They are numbers that are not rational.
They want us to find the complement of set A.
Well... what is the complement? The complement of a set is everything in the entire universe that is NOT in set A.
If we are told that our set A are irrational, or not rational, numbers, and we have to find all of the other real numbers that are NOT apart of that set, what would we call the numbers that are NOT irrational? Those would be rational numbers!
Therefore, we can write the complement of set A, or commonly written as set A', as:
A'= {rational numbers}.
***NOTE***Of course I have written this in word form to match what has been presented in the question, it is very important to read the instructions and make sure they are not asking for the answer to be written in set-builder notation, for higher grade classes you would write the complement of A as:
A'={x:x is rational}
or to be more specific...
A'= {(p/q):p^q∈Z, p^q≠0}
Reading the instructions, and identifying what definitions are being used helps a lot with these types of questions. I hope this helped!