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 (Ib)a*b=b*a [B2] Distributive laws: (2a)a+(b*c)=(a+b)*(a+c) (2b)a*(b+c)=(a米b)+(a*c) [B3] Identity laws: (3a)a+0=a (3b)a*1=a [Ba] 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: [L1】Commutative law: (1a)aAb=b入d (Ib)avb=bva [L2]Associative law: (2a)(4八b)Ac=aA(bAc) (2b)(avb)vc=av(bvc) [L3]Absorption law: (34)4A(aVb)=a (3b)aV(a入b)=4 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？