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Determine whether set [tex]B[/tex] is a subset of set [tex]A[/tex].
[tex]\[
\begin{aligned}
A & = \{0, 1, 2, 3, 4\} \\
B & = \{1, 2\}
\end{aligned}
\][/tex]
To determine whether set [tex]\( B \)[/tex] is a subset of set [tex]\( A \)[/tex], we need to verify if every element in set [tex]\( B \)[/tex] is also an element in set [tex]\( A \)[/tex].
Given: [tex]\[ A = \{0, 1, 2, 3, 4\} \][/tex] [tex]\[ B = \{1, 2\} \][/tex]
Let's check each element of set [tex]\( B \)[/tex]:
1. The first element of [tex]\( B \)[/tex] is 1. - We look for 1 in set [tex]\( A \)[/tex]. - Set [tex]\( A \)[/tex] contains the element 1.
2. The second element of [tex]\( B \)[/tex] is 2. - We look for 2 in set [tex]\( A \)[/tex]. - Set [tex]\( A \)[/tex] contains the element 2.
Since all the elements of set [tex]\( B \)[/tex] (which are 1 and 2) are also found in set [tex]\( A \)[/tex], we conclude that:
[tex]\[ B \subseteq A \][/tex]
Therefore, set [tex]\( B \)[/tex] is indeed a subset of set [tex]\( A \)[/tex].
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