Let's solve the problem step by step to determine how many subsets the set [tex]\( A = \{a, b, c\} \)[/tex] has, including the empty set [tex]\( \emptyset \)[/tex].
1. Determine the number of elements in the set [tex]\( A \)[/tex]:
The set [tex]\( A \)[/tex] contains the elements [tex]\( \{a, b, c\} \)[/tex].
Thus, the number of elements [tex]\( n \)[/tex] in the set [tex]\( A \)[/tex] is:
[tex]\[
n = 3
\][/tex]
2. Calculate the total number of subsets:
The number of subsets of a set with [tex]\( n \)[/tex] elements is given by [tex]\( 2^n \)[/tex]. This includes all possible combinations of elements, ranging from the empty set to the set itself.
Given [tex]\( n = 3 \)[/tex], we calculate:
[tex]\[
2^3 = 8
\][/tex]
Therefore, the set [tex]\( A = \{a, b, c\} \)[/tex] has [tex]\( 8 \)[/tex] subsets in total, including the empty set [tex]\( \emptyset \)[/tex].
