MathDB

8

Part of 2023 AMC 12/AHSME

Problems(1)

Cardinality is the Least Element

Source: 2023 AMC 12B #8

11/15/2023
How many nonempty subsets BB of {0,1,2,3,…,12}\{0, 1, 2, 3, \dots, 12\} have the property that the number of elements in BB is equal to the least element of BB? For example, B={4,6,8,11}B = \{4, 6, 8, 11\} satisfies the condition.
<spanclass=′latex−bold′>(A)</span> 256<spanclass=′latex−bold′>(B)</span> 136<spanclass=′latex−bold′>(C)</span> 108<spanclass=′latex−bold′>(D)</span> 144<spanclass=′latex−bold′>(E)</span> 156<span class='latex-bold'>(A)</span>\ 256 \qquad<span class='latex-bold'>(B)</span>\ 136 \qquad<span class='latex-bold'>(C)</span>\ 108 \qquad<span class='latex-bold'>(D)</span>\ 144 \qquad<span class='latex-bold'>(E)</span>\ 156
AMCAMC 122023 AMC2023 AMC 12B