Assess the following definitions by trying to find counterexamples. State whether your counterexample(s) show the definition is too broad or too narrow or both, and make it clear which counterexample shows which flaw in the definition. If you cannot find counterexamples, explain why.
(a) A hope is a wish concerning the future.
(b) X is a sphere if and only if X is a three-dimensional figure.
(c) X is a democracy if and only if X holds popular elections.