A counterexample is an example that runs counter to (opposes) a generalization, thus falsifying it A TV newscast that limited its coverage of "mayhem and misery" (in Bob Inman's phrase) would falsify a claim that all local TV newscasts focused on crime and disasters Consequently, careful thinkers avoid rash generalizations (see hasty generalization) by qualifying their generalizations If there are local TV newscasts that do not focus on "mayhem and misery," one could say, "Most local TV newscasts focus on "mayhem and misery "