MathDB
Logical statements

Source: 1959 AHSME Problem 47

August 14, 2013
AMC

Problem Statement

Assume that the following three statements are true: II. All freshmen are human. IIII. All students are human. IIIIII. Some students think. Given the following four statements: <spanclass=latexbold>(1)</span> All freshmen are students. <span class='latex-bold'>(1)</span>\ \text{All freshmen are students.}\qquad <spanclass=latexbold>(2)</span> Some humans think.<span class='latex-bold'>(2)</span>\ \text{Some humans think.}\qquad <spanclass=latexbold>(3)</span> No freshmen think.<span class='latex-bold'>(3)</span>\ \text{No freshmen think.}\qquad <spanclass=latexbold>(4)</span> Some humans who think are not students.<span class='latex-bold'>(4)</span>\ \text{Some humans who think are not students.} Those which are logical consequences of I,II, and III are: <spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 2,3<spanclass=latexbold>(D)</span> 2,4<spanclass=latexbold>(E)</span> 1,2 <span class='latex-bold'>(A)</span>\ 2\qquad<span class='latex-bold'>(B)</span>\ 4\qquad<span class='latex-bold'>(C)</span>\ 2,3\qquad<span class='latex-bold'>(D)</span>\ 2,4\qquad<span class='latex-bold'>(E)</span>\ 1,2