MathDB
Converse and Inverse of Statement

Source: 1959 AMC 12 Problem 6

August 13, 2013
geometryrectangleAMC

Problem Statement

Given the true statement: If a quadrilateral is a square, then it is a rectangle. It follows that, of the converse and the inverse of this true statement is: <spanclass=latexbold>(A)</span> only the converse is true<spanclass=latexbold>(B)</span> only the inverse is true <spanclass=latexbold>(C)</span> both are true <span class='latex-bold'>(A)</span>\ \text{only the converse is true} \qquad<span class='latex-bold'>(B)</span>\ \text{only the inverse is true }\qquad <span class='latex-bold'>(C)</span>\ \text{both are true} \qquad <spanclass=latexbold>(D)</span> neither is true<spanclass=latexbold>(E)</span> the inverse is true, but the converse is sometimes true<span class='latex-bold'>(D)</span>\ \text{neither is true} \qquad<span class='latex-bold'>(E)</span>\ \text{the inverse is true, but the converse is sometimes true}