To find the intersection of two sets [tex]\( E \)[/tex] and [tex]\( F \)[/tex], denoted as [tex]\( E \cap F \)[/tex], we need to identify the elements that are common to both sets.
Given:
[tex]\[ E = \{2, 3, 5, 8, 9, 11, 20, 43\} \][/tex]
[tex]\[ F = \{2, 4, 8, 12, 32, 43, 50\} \][/tex]
Now, we will list the elements that are present in both [tex]\( E \)[/tex] and [tex]\( F \)[/tex]:
1. The number [tex]\( 2 \)[/tex] is in both [tex]\( E \)[/tex] and [tex]\( F \)[/tex].
2. The number [tex]\( 8 \)[/tex] is in both [tex]\( E \)[/tex] and [tex]\( F \)[/tex].
3. The number [tex]\( 43 \)[/tex] is in both [tex]\( E \)[/tex] and [tex]\( F \)[/tex].
Thus, the elements {2, 8, 43} are common to both sets.
Therefore, the intersection [tex]\( E \cap F \)[/tex] is:
[tex]\[ E \cap F = \{2, 8, 43\} \][/tex]
From the provided options, the correct intersection set is:
[tex]\[ \{2, 8, 43\} \][/tex]
Note that one of the choices has a set notation error; it mistakenly uses a parenthesis instead of a curly bracket. The correct notation should be:
[tex]\[ \{2, 8, 43\} \][/tex]
Thus, the correct answer is:
[tex]\[ \{2, 8, 43\} \][/tex]
