Discussion
The number of non-empty subsets of X = {1, 2, 3, 4, 5, 6, 7} containing only even integers is :
Answer: A
There are 7 such subsets.
The even integers in X are 2, 4 and 6. A subset containing only even integers is any subset of {2, 4, 6}, and excluding the empty set leaves
\[ 2^{3} - 1 = 7 \]
They are {2}, {4}, {6}, {2, 4}, {2, 6}, {4, 6} and {2, 4, 6}. The answer 8 counts the empty set as well, which the question excludes; 3 counts only the even numbers themselves, and 1 counts only the full set {2, 4, 6}.
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