Let's determine the correct subset symbol to use for the sets [tex]\(\{-5,0,4\}\)[/tex] and [tex]\(\{-9,6,8,3,0\}\)[/tex].
Consider the set [tex]\(\{-5,0,4\}\)[/tex]. For this set to be a subset of [tex]\(\{-9,6,8,3,0\}\)[/tex], every element in [tex]\(\{-5,0,4\}\)[/tex] must also be an element in [tex]\(\{-9,6,8,3,0\}\)[/tex].
Let's check each element of [tex]\(\{-5,0,4\}\)[/tex] one by one:
- The first element in [tex]\(\{-5,0,4\}\)[/tex] is [tex]\(-5\)[/tex]. Checking [tex]\(\{-9,6,8,3,0\}\)[/tex], we see that [tex]\(-5\)[/tex] is not present in this set.
- Since [tex]\(-5\)[/tex] is not in [tex]\(\{-9,6,8,3,0\}\)[/tex], we can immediately conclude that [tex]\(\{-5,0,4\}\)[/tex] is not a subset of [tex]\(\{-9,6,8,3,0\}\)[/tex].
Therefore, the correct symbol to insert is [tex]\(\not\subset\)[/tex].
The statement is:
[tex]\[
\{-5,0,4\} \not\subset \{-9,6,8,3,0\}
\][/tex]
