《离散数学》题库及答案

?(?P??Q)?(?P?Q)?(P??Q)?(P?Q)(主析取范式)

6、?(P→Q)?(R?P)

解: ?(P→Q)?(R?P)??(?P?Q)?(R?P)

?(P??Q)?(R?P)(析取范式) ?(P??Q?(R??R))?(P?(?Q?Q)?R)

?(P??Q?R)?(P??Q??R)?(P??Q?R)?(P?Q?R) ?(P??Q?R)?(P??Q??R)?(P?Q?R)(主析取范式)

?(?(P→Q)?(R?P))?(P?Q??R)?(?P?Q?R)?(?P??Q?R)

? (?P??Q??R)?(?P?Q??R)(原公式否定的主析取范式)

?(P→Q)?(R?P)?(?P??Q?R)?(P??Q??R)?(P?Q??R)

?(P?Q?R)?(P??Q?R)(主合取范式)

7、P?(P→Q)

解:P?(P→Q)?P?(?P?Q)?(P??P)?Q

?T(主合取范式)

?(?P??Q)?(?P?Q)?(P??Q)?(P?Q)(主析取范式)

8、(R→Q)?P

解:(R→Q)?P?(?R?Q )?P

? (?R?P)?(Q?P) (析取范式) ? (?R?(Q??Q)?P)?((?R?R)?Q?P)

?(?R?Q?P)?(?R??Q?P)?(?R?Q?P)?(R?Q?P) ?(P?Q??R)?(P??Q??R)?(P?Q?R)(主析取范式)

?((R→Q)?P)?(?P??Q??R)?(?P?Q??R)?(P??Q?R)

?(?P?Q?R)?(?P??Q?R)(原公式否定的主析取范式)

(R→Q)?P?(P?Q?R)?(P??Q?R)?(?P?Q??R)

?(P??Q??R)?(P?Q??R)(主合取范式)

9、P→Q

解:P→Q??P?Q(主合取范式)

?(?P?(Q??Q))?((?P?P)?Q)

?(?P?Q)?(?P??Q)?(?P?Q)?(P?Q)

13

?(?P?Q)?(?P??Q)?(P?Q)(主析取范式)

10、 P??Q

解: P??Q (主合取范式)

?(P?(?Q?Q))?((?P?P)??Q) ?(P??Q)?(P?Q)?(?P??Q)?(P??Q) ?(P??Q)?(P?Q)?(?P??Q)(主析取范式)

11、P?Q

解:P?Q(主析取范式)?(P?(Q??Q))?((P??P)?Q)

?(P??Q)?(P?Q)?(P?Q)?(?P?Q) ?(P??Q)?(P?Q)?(?P?Q)(主合取范式)

12、(P?R)?Q

解:(P?R)?Q

??(P?R)?Q ?(?P??R)?Q

?(?P?Q)?(?R?Q)(合取范式) ?(?P?Q?(R??R))?((?P?P)?Q??R)

?(?P?Q?R)?(?P?Q??R)?(?P?Q??R)?(P?Q??R) ?(?P?Q?R)?(?P?Q??R)?(?P?Q??R)?(P?Q??R) ?(?P?Q?R)?(?P?Q??R)?(P?Q??R)(主合取范式) ?(P?R)?Q

?(?P??Q?R)?(?P??Q??R)?(P?Q?R)?(P??Q?R)?(P??Q??R)

(原公式否定的主析取范式)

(P?R)?Q

?(P?Q??R)?(P?Q?R)?(?P??Q??R)?(?P?Q??R)

?(?P?Q?R)(主析取范式)

13、(P?Q)?R

解:(P?Q)?R

??(?P?Q)?R ?(P??Q)?R(析取范式)

14

?(P??Q?(R??R))?((P??P)?(Q??Q)?R)

?(P??Q?R)?(P??Q??R)?(P?Q?R)?(P??Q?R)?(?P?Q?R)

?(?P??Q?R)

?(P??Q?R)?(P??Q??R)?(P?Q?R)?(?P?Q?R)

?(?P??Q?R)(主析取范式)

(P?Q)?R

??(?P?Q)?R ?(P??Q)?R(析取范式) ?(P?R)?(?Q?R)(合取范式)

?(P?(Q??Q)?R)?((P??P)??Q?R)

?(P?Q?R)?(P??Q?R)?(P??Q?R)?(?P??Q?R) ?(P?Q?R)?(P??Q?R)?(?P??Q?R)(主合取范式)

14、(P?(Q?R))?(?P?(?Q??R))

解:(P?(Q?R))?(?P?(?Q??R))

?(?P?(Q?R))?(P?(?Q??R))

?(?P?Q)?(?P?R)?(P??Q)?(P??R)(合取范式) ?(?P?Q?(R??R))?(?P?(Q??Q)?R)?(P??Q?(R??R))

?(P?(Q??Q)??R)

?(?P?Q?R)?(?P?Q??R)?(?P?Q?R)?(?P??Q?R)

?(P??Q?R)?(P??Q??R)?(P?Q??R)?(P??Q??R)

?(?P?Q?R)?(?P?Q??R)?(?P??Q?R)?(P??Q?R)

?(P?Q??R)?(P??Q??R)(主合取范式)

?(P?(Q?R))?(?P?(?Q??R))

?(?P??Q??R)?(P?Q?R)(原公式否定的主合取范式) (P?(Q?R))?(?P?(?Q??R))

?(P?Q?R)?(?P??Q??R)(主析取范式)

15、P?(?P?(Q?(?Q?R)))

解:P?(?P?(Q?(?Q?R)))

? P?(P?(Q?(Q?R)))

15

? P?Q?R(主合取范式) ?(P?Q?R)

?(P??Q?R)?(P??Q??R)?(P?Q??R)?(?P?Q?R)

?(?P?Q??R)?(?P??Q?R)?(?P??Q??R)

(原公式否定的主合取范式)

(P?Q?R)

?(?P?Q??R)?(?P?Q?R)?(?P??Q?R)?(P??Q??R)

?(P??Q?R)?(P?Q??R)?(P?Q?R)(主析取范式)

16、(P?Q)?(P?R)

解、(P?Q)?(P?R)

?(?P?Q)?(?P?R) (合取范式) ?(?P?Q?(R??R)?(?P?(?Q?Q)?R)

?(?P?Q?R)?(?P?Q??R)?(?P??Q?R)?(?P?Q?R) ?(?P?Q?R)?(?P?Q??R)?(?P??Q?R)(主合取范式) (P?Q)?(P?R)

?(?P?Q)?(?P?R) ??P?(Q?R)(合取范式)

?(?P?(Q??Q)?(R??R))?((?P?P)?Q?R)

?(?P?Q?R)?(?P??Q?R)?(?P?Q??R)?(?P??Q?R)

?(?P?Q?R)?(P?Q?R)

?(?P?Q?R)?(?P??Q?R)?(?P?Q??R)?(?P??Q?R)?(P?Q?R)

(主析取范式)

三、证明:

1、P→Q,?Q?R,?R,?S?P=>?S

证明:

(1) ?R 前提 (2) ?Q?R 前提 (3) ?Q (1),(2)

16

联系客服:779662525#qq.com(#替换为@)