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  "body": "\n## Summary\n\nA counterexample to a universal statement $\\forall x \\in X, \\, P(x)$ is an element $a \\in X$ such that $P(a)$ is false.\nOne counterexample shows that the universal statement is false.\n\n## Remarks\n\nThe number $2$ is a counterexample to \"each prime number is odd\".\nThis works because of the [[negation of a universal statement|0P3A06QNDP]]: $\\neg \\forall x \\, P(x)$ is equivalent to $\\exists x \\, \\neg P(x)$.\n\n## Explanations\n\n### L1 human\n\nTo show that a general claim is wrong, one bad case is enough.\n\"Each continuous function is differentiable\" is false: $f(x) = |x|$ is continuous but not differentiable at $0$.\n",
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