问题1：这个是布尔代数的定义，你有没有一种熟悉的感 觉？它和另一个定义有什么异同之处？你能想到什么？ Let B be a nonempty set with two binary operations and *a unary operation',and two distinct elements 0 and 1.Then B is called a Boolean algebra if the following axioms hold where a.b.c are any elements in B: [B:] Commutative laws: (la)a+b=b+a (1b) a*b=b米a [B2] Distributive laws: (2a)a+(b*c)=(a+b)*(a+c) (2b) a*(b+c)=(a*b)+(a*c) [Ba] Identity laws: (3a)a+0=a (3b) a*1=a B Complement laws: (4a)a+a'=1 (4b)a*a=0 Axioms Defining a Lattice Let L be a nonempty set closed under two binary operations called meer and join,denoted respectively by A and v.Then L is called lattice if the following axioms hold where a,b.c are elements in L: [LI]Commutative law: (1a)a八b=bAa (1b)avb=bva [L2]Associative law: (2a)(aAb)Ac=a(bA e) (2b)(av b)vc=av(bv e) [L3]Absorption law: (3a)a (avb)=a (3b)av(aAb)=a We will sometimes denote the lattice by (L.A,V)when we want to show which operations are involved.问题1：这个是布尔代数的定义，你有没有一种熟悉的感 觉?它和另一个定义有什么异同之处？你能想到什么？