논리식 구하기

논리식 구하기  ∧ ∨ → ↔  =

논리식 만들기 • [연습] 다음의 기호를 사용하여 아래의 복합명제를 논리식으로 만드시오. • J = John dances. J' = John is happy. • M = Mary dances. M' = Mary is happy • B = Bill dances. B' = Bill is happy. • 1) John is dancing but Mary is not dancing. • 2) If John does not dance, then Mary will not be happy. • 3) John's dancing is sufficient to make Mary happy. • 4) John's dancing is necessary to make Mary happy. • 5) John will not dance unless Mary is happy. • 6) If John's dancing is necessary for Mary to be happy, Bill will be happy. • 7) If Mary dances although John is not happy, Bill will dance. • 8) If neither John nor Bill is dancing, Mary is not happy. • 9) Mary is not happy unless either John or Bill is dancing. • 10) Mary will be happy if both John and Bill dance. • 11) Although neither John nor Bill is dancing, Mary is happy. • 12) If Bill dances, then if Mary dances John will too. • 13) Mary will be happy, only if Bill is happy. • 14) Neither John nor Bill will dance ,if Mary is not happy. • 15) If Mary dances, then John dances only if Bill dances. • 16)* Mary will dance, if John or Bill but not both dance. • 17) If John dances and so does Mary, but Bill does not, then Mary will not be happy but John and Bill will. • 18) Mary will be happy, if and only if John is happy. • 19) Provided that Bill is unhappy, John will not dance unless Mary is dancing. (ꍃB'→ (ꍃJ v M)) . • 20) If John dances on the condition that if he dances then Mary dances, then he dances. ((J → M) → J) → J)

[연습] 다음의 기호를 사용하여 아래의 복합명제를 논리식으로 만드시오. J = John dances. J' = John is happy. M = Mary dances. M' = Mary is happy B = Bill dances. B' = Bill is happy.

1) John is dancing but Mary is not dancing. J ∧  M 2) If John does not dance, then Mary will not be happy.  J → M’ 3) John's dancing is sufficient to make Mary happy. J → M’  ∧ ∨ → ↔  =

4) John's dancing is necessary to make Mary happy M’ → J 5) John will not dance unless Mary is happy. M’ ∨  J, M’→ J 6) If John's dancing is necessary for Mary to be happy, Bill will be happy. (M → J) → B’ ∧ → ↔  =

7) If Mary dances although John is not happy, Bill will dance. 8) If neither John nor Bill is dancing, Mary is not happy. 9) Mary is not happy unless either John or Bill is dancing. J’∧ M → B  (J ∨ B) →  M’ ( J ∨ B)∨ M’  ( J ∨ B)→ M’ 이하 생략 ∧ ∨ → ↔  =

10) Mary will be happy if both John and Bill dance. 11) Although neither John nor Bill is dancing, Mary is happy. 12) If Bill dances, then if Mary dances John will too. 13) Mary will be happy, only if Bill is happy. 14) Neither John nor Bill will dance ,if Mary is not happy. 15) If Mary dances, then John dances only if Bill dances. 16)* Mary will dance, if John or Bill but not both dance. 17) If John dances and so does Mary, but Bill does not, then Mary will not be happy but John and Bill will. 18) Mary will be happy, if and only if John is happy. 19) Provided that Bill is unhappy, John will not dance unless Mary is dancing. (ꍃB'→ (ꍃJ v M)) . 20) If John dances on the condition that if he dances then Mary dances, then he dances. ((J → M) → J) → J)

논리식 구하기