1 习题参考解答 习题1 .1 1、(3)P:银行利率降低 Q:股价没有上升 P∧Q (5) P:他今天乘火车去了北京 Q:他随旅行团去了九寨沟 QP (7) P:不识庐山真面目 Q:身在此山中 Q→P,或 ~P→~Q (9) P:一个整数能被 6 整除 Q:一个整数能被 3 整除 R:一个整数能被 2 整除 T:一个整数的各位数字之和能被 3 整除 P→Q∧R ,Q→T 2、(1)T (2)F (3)F (4)T (5)F (6)T (7)F (8)悖论 习题 1 .3 1(3) )()()()()()(RPQPRPQPRQPRQP 2 (4) ()()()(())()(()())(())()()()()PQQRRPPRQRPPRRPQRPPRPRQRQP 右 2、不, 不, 能 习题 1.4 1 (3) (())~((~))(~)( )~(~(~))(~~ )(~)PRQPPRQPPRTPRPRQQPRQPRQ、 主合取范式 )()()()()()()()()()()()()()())(())(()()(())()())(()((QPRPQRPQRRQPRQPRQPQPRQPRPQRPQRRQPRQPRQPRQPQQPRPPQRRRQQPPRQRPPQRPPQRP ————主析取范式 (2) ()()(~)(~)(~(~))(~(~))(~~ )(~)(~~ )PQPRPQPRPQRRPRQQPQRPQRPRQ2、 ()~()(~)(~)(~~ )(~)(~~ )PQRPQRPQPRPQRPQRPRQ 等价 3、解:根据给定的条件有下述命题公式: (A→(CD))∧~(B∧C)∧~(C∧D) (~A∨(C∧~D)∨(~C∧D))∧(~B∨~C)∧(~C∨~D) ((~A∧~B)∨(C∧~D∧~B)∨(~C∧D∧~B)∨ (~A∧~C)∨(C∧~D∧~C)∨(~C∧D∧~C))∧(~C∨~D) 3 ((~A∧~B)∨(C∧~D∧~B)∨(~C∧D∧~B)∨ (~A∧~C)∨(~C∧D∧~C)) ∧(~C∨~D) (~A∧~B∧~C)∨(C∧~D∧~B∧~C)∨(~C∧D∧~B∧~C)∨ (~A∧~C∧~C)∨(~C∧D∧~C∧~C)∨(~A∧~B∧~D)∨ (C∧~D∧~B∧~D)∨(~C∧D∧~B∧~D)∨(~A∧~C∧~D)∨ (~C∧D∧~C∧~D)(由题意和矛盾律) (~C∧D∧~B)∨(~A∧~C)∨(~C∧D)∨(C∧~D∧~B) (...