命题逻辑等值演算.doc

命题逻辑等值演算
County continuation records has examined and approved the draft, spirit, believe, comprehensive YearboR)∨P (Q∨P)∧(R∨P)
(P∨Q∨R)∧(P∨Q∨R)∧(P∨Q∨R)
M0∧M1∧M3 (主合取范式)
则其主析取范式为m2∨m4∨m5∨m6∨m7
例5 . 用等值演算法证明下面等值式。
P (P∧Q)∨(P∧Q)
(PQ)∧(PR) P(Q∧R)
(PQ) (P∨Q)∧(P∧Q)
(P∧Q)∨(P∧Q) (P∨Q)∧(P∧Q)
解: (1) 右边 P∧(P∨Q)∧(P∨Q)∧(Q∨Q)
P∧(P∨Q∧Q)∧T
P∧P
P 左边
所以P (P∧Q)∨(P∧Q)
(2) 左边 (P∨Q)∧(P∨R)
P∨Q∧R
P(Q∧R) 右边
所以(PQ)∧(PR) P(Q∧R)
(3) 左边 ((PQ)∧(QP))
(P∨Q)∨(Q∨P)
P∧Q∨Q∧P
(P∨Q)∧(P∨P)∧(Q∨Q)∧(Q∨P)
(P∨Q)∧(Q∨P)
(P∨Q)∧(P∧Q)
右边
County continuation records has examined and approved the draft, spirit, believe, comprehensive Yearbook of zhuanglang already prepared draft, entered the phase of evaluation. Civil air defense work
County continuation records has examined and approved the draft, spirit, believe, comprehensive Yearbook of zhuanglang already prepared draft, entered the phase of evaluation. Civil air defense work
County continuation records has examined and approved the draft, spirit, believe, comprehensive Yearbook of zhuanglang already prepared draft, entered the phase of evaluation. Civil air defense work
所以(PQ) (P∨Q)∧(P∧Q)
(4) 左边 (P∧Q)∨(P∧Q)
(P∨P)∧(P∨Q)∧(Q∨P)∧(Q∨Q)
(P∨Q)∧(Q∨P)
(P∨Q)∧(P∧Q)
右边
所以 (P∧Q)∨(P∧Q) (P∨Q)∧(P∧Q)
例6 . 将下列公式化成与之等值且只含{,∨, ∧}中联结词的公式。
(1) ( P(Q(Q∧R)))
(2)