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  "body": "\n## Definition\n\nLet $X$ be a set.\nA predicate on $X$ is a statement $P(x)$ with a variable $x$ that ranges over $X$, such that $P(a)$ is a [[proposition|0ZGC7ZESYN]] for each $a \\in X$.\nMore generally, a predicate $P(x_1, \\dots, x_n)$ has $n$ variables, and $n$ is its arity.\n\n## Remarks\n\nThe predicate \"$x \u003e 3$\" on the integers gives the true proposition \"$5 \u003e 3$\" and the false proposition \"$1 \u003e 3$\".\nA predicate on $X$ determines the set $\\{x \\in X \\mid P(x)\\}$ of the values that make it true. See [[set-builder notation|0TMZ89Q5KA]].\nA predicate with two variables is a [[binary relation|08EJC6Q25H]].\n\n## Explanations\n\n### L1 human\n\nA predicate is a sentence with a blank, such as \"___ is prime\".\nIt is not true or false yet.\nWhen you fill the blank with a number, you get a proposition.\n",
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