Let's solve the given problems step-by-step. The sets provided are as follows:
[tex]\[ M = \{-2, 0, 1, 7, 8\} \][/tex]
[tex]\[ F = \{-2, -1, 2, 6\} \][/tex]
First, let's find the intersection of the sets [tex]\(M\)[/tex] and [tex]\(F\)[/tex].
### Intersection of [tex]\(M\)[/tex] and [tex]\(F\)[/tex]
The intersection of two sets [tex]\(M\)[/tex] and [tex]\(F\)[/tex] is a set containing all elements that are both in [tex]\(M\)[/tex] and in [tex]\(F\)[/tex].
By inspecting the two sets [tex]\(M\)[/tex] and [tex]\(F\)[/tex] we see the common elements:
[tex]\[M \cap F: \{-2\} \][/tex]
So,
[tex]\[ M \cap F = \{-2\} \][/tex]
### Union of [tex]\(M\)[/tex] and [tex]\(F\)[/tex]
The union of two sets [tex]\(M\)[/tex] and [tex]\(F\)[/tex] is a set containing all elements that are in [tex]\(M\)[/tex], in [tex]\(F\)[/tex], or in both.
By combining all unique elements from both [tex]\(M\)[/tex] and [tex]\(F\)[/tex] we get:
[tex]\[M \cup F: \{-2, 0, 1, 7, 8, -1, 2, 6\} \][/tex]
So,
[tex]\[ M \cup F = \{0, 1, 2, 6, 7, 8, -1, -2\} \][/tex]
Putting it all together, we have:
[tex]\[
\begin{array}{l}
M \cap F = \{-2\} \\
M \cup F = \{0, 1, 2, 6, 7, 8, -1, -2\}
\end{array}
\][/tex]
