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].
