证明(p∧¬q)∨(¬p∧q) ⇔ (p∨q)∧¬(p∧q)?

问题描述:

证明(p∧¬q)∨(¬p∧q) ⇔ (p∨q)∧¬(p∧q)?

2种方法
1.图表法,你把所有表达式的真值情况全都列出,这个比较麻烦,但是很直观
2. 恒等法
(p∧¬q)∨(¬p∧q)
=[(p∧¬q)∨¬p]∧[(p∧¬q)∨q] -------Distributive laws
=[(p∨¬p)∧(¬q∨¬p)]∧[(p∨q)∧(¬q∨q)] ------Distributive laws
=[T∧(¬q∨¬p)]∧[(p∨q)∧T] ------ Negation laws
=(¬q∨¬p)∧(p∨q)------- Identity laws
=(p∨q)∧(¬q∨¬p) ------Commutative laws
=(p∨q)∧¬(p∧q) -------De Morgan's laws