MathDB
Equivalency of a Theorem

Source:

June 8, 2009

Problem Statement

Start with the theorem "If two angles of a triangle are equal, the triangle is isosceles," and the following four statements: 1. If two angles of a triangle are not equal, the triangle is not isosceles. 2. The base angles of an isosceles triangle are equal. 3. If a triangle is not isosceles, then two of its angles are not equal. 4. A necessary condition that two angles of a triangle be equal is that the triangle be isosceles. Which combination of statements contains only those which are logically equivalent to the given theorem? <spanclass=latexbold>(A)</span> 1,2,3,4<spanclass=latexbold>(B)</span> 1,2,3<spanclass=latexbold>(C)</span> 2,3,4<spanclass=latexbold>(D)</span> 1,2<spanclass=latexbold>(E)</span> 3,4 <span class='latex-bold'>(A)</span>\ 1,\,2,\,3,\,4 \qquad <span class='latex-bold'>(B)</span>\ 1,\,2,\,3\qquad <span class='latex-bold'>(C)</span>\ 2,\,3,\,4\qquad <span class='latex-bold'>(D)</span>\ 1,\,2\qquad <span class='latex-bold'>(E)</span>\ 3,\,4