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  "body": "\n## Definition\n\nLet $p$ and $q$ be [[propositions|0ZGC7ZESYN]].\nThe biconditional of $p$ and $q$ is the proposition $p \\leftrightarrow q$, read \"$p$ if and only if $q$\".\nThe proposition $p \\leftrightarrow q$ is true when $p$ and $q$ are both true or both false. Otherwise, it is false.\n\n| $p$ | $q$ | $p \\leftrightarrow q$ |\n|---|---|---|\n| T | T | T |\n| T | F | F |\n| F | T | F |\n| F | F | T |\n\n## Remarks\n\nOther notations are $p \\Leftrightarrow q$ and \"$p$ iff $q$\".\nThe proposition $p \\leftrightarrow q$ has the same truth value as $(p \\to q) \\land (q \\to p)$.\n\n## Explanations\n\n### L1 human\n\n\"A triangle has three equal sides if and only if it has three equal angles\" is a biconditional.\nIt says two things: each property gives the other.\nTo prove a biconditional, you usually prove the two [[implications|0ZNX6DQ3EJ]] separately.\n",
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