Question

Find the complement of set A in universe U.

U is the set of whole numbers less than 10.
A is the set of factors of 9.

Answer 1

So:
\[U=\left\{ x \in \mathbb{N} \ | \ x<10\right\}\] (read as the set of natural numbers x such that x is less than 10 or the set of all natural numbers less than 10)
& \[A=\left\{ x,y \in \mathbb{N} \ | \ x=\frac{9}{y}\right\}\] This one was a bit trickier to write out since I am a bit rusty but by this I mean x and y are natural numbers and the only way for the given relationship to hold x=9/y is if y =1,3,9 (i.e. the factors of 9). If y were something else x would cease to be a natural number and hence wouldnt be in the set. But sorry for going into such detail but I wanted to ensure this notation made sense.

Answer 2

So we want the complement of A within U. Well the complement of A (within U) will be all those natural numbers that are less than 10, but not factors of 9 (i.e. not 1,3,9).

Btw sorry I kept saying natural numbers when the problem specified whole numbers. The two sets are exactley the same except for the choice to include 0 or not. I will leave it up to you whether you answer contains this or not. It depends on the class or teacher, but I have heard both sides (Naturals contain zero and Wholes do not or Wholes contain zero and naturals do not). Personally I ditch the whole numbers and just do with the natural numbers, which I take to include zero. Please use the convention that is used for your class! :D