Sure! Let's analyze the given problem step-by-step:
1. The problem provides a set of elements: [tex]\(\{4, 6, 8, 9\}\)[/tex].
2. It asks about the membership of the element [tex]\(5\)[/tex] in this set.
3. We need to determine whether 5 is an element of the set [tex]\(\{4, 6, 8, 9\}\)[/tex] and fill in the blank accordingly.
Let's see each choice:
Choice A: The symbol should be used because 5 is not an element of the set.
Choice B: The symbol ∈ should be used because [tex]\(\{4, 6, 8, 9\}\)[/tex] and 5 are equal sets.
- This option is not valid because [tex]\(\{4, 6, 8, 9\}\)[/tex] and [tex]\(5\)[/tex] are not sets, let alone equal sets.
Choice C: The symbol ∉ should be used because [tex]\(\{4, 6, 8, 9\}\)[/tex] is a set and none of the elements in 5 is a s...
- This option doesn't make sense due to incomplete reasoning and misinterpretation of sets and elements.
Choice D: The symbol ∉ should be used because 5 is not an element of the set.
- This matches our need to show that 5 is not within the set [tex]\(\{4, 6, 8, 9\}\)[/tex].
Choice E: The symbol ∈ should be used because ...
- The statement is incomplete and thus unsuitable.
Choice F: The symbol ∈ should be used because 5 is an element of the set.
- This is incorrect because 5 is not one of the elements in [tex]\(\{4, 6, 8, 9\}\)[/tex].
Given our analysis, the correct answer is:
Choice A: The symbol ∉ should be used because 5 is not an element of the set.
So, we choose option A.
