MathDB
Subset Logic

Source: 2022 AMC 10B #14

November 17, 2022
2022 AMC 10BAMCAMC 102022 AMCSets

Problem Statement

Suppose that SS is a subset of {1,2,3,...,25}\{1, 2, 3,...,25\} such that the sum of any two (not necessarily distinct) elements of SS is never an element of SS. What is the maximum number of elements SS may contain?
<spanclass=latexbold>(A)</span>12<spanclass=latexbold>(B)</span>13<spanclass=latexbold>(C)</span>14<spanclass=latexbold>(D)</span>15<spanclass=latexbold>(E)</span>16<span class='latex-bold'>(A) </span>12 \qquad <span class='latex-bold'>(B) </span>13 \qquad <span class='latex-bold'>(C) </span>14 \qquad <span class='latex-bold'>(D) </span>15 \qquad <span class='latex-bold'>(E) </span>16