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  "body": "\n## Definition\n\nA Boolean algebra is a set $A$ with two binary operations $\\wedge$ and $\\vee$, a unary operation $\\neg$, and two elements $0, 1 \\in A$.\nThese axioms must hold for all $a, b, c \\in A$.\nAssociativity: $a \\vee (b \\vee c) = (a \\vee b) \\vee c$ and $a \\wedge (b \\wedge c) = (a \\wedge b) \\wedge c$.\nCommutativity: $a \\vee b = b \\vee a$ and $a \\wedge b = b \\wedge a$.\nAbsorption: $a \\vee (a \\wedge b) = a$ and $a \\wedge (a \\vee b) = a$.\nIdentity: $a \\vee 0 = a$ and $a \\wedge 1 = a$.\nDistributivity: $a \\vee (b \\wedge c) = (a \\vee b) \\wedge (a \\vee c)$ and $a \\wedge (b \\vee c) = (a \\wedge b) \\vee (a \\wedge c)$.\nComplements: $a \\vee \\neg a = 1$ and $a \\wedge \\neg a = 0$.\n\n## Remarks\n\nThe relation $a \\le b$, defined by $a \\wedge b = a$, is a partial order with least element $0$ and greatest element $1$.\nEquivalently, a Boolean algebra is a complemented [[distributive lattice|0T36P6TXQ6]].\nThe power set of a set is a Boolean algebra, the [[power set Boolean algebra|004J7ZEFAT]]. Boolean algebras correspond to [[Boolean rings|0N5FCV2YV6]].\n\n## Explanations\n\n### L1 human\n\nA Boolean algebra has operations that behave like and, or and not on true and false, or like intersection, union and complement on sets.\nIts axioms are the common rules of logic and of set algebra.\n",
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