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Either it is not the case that Gonzolo play music and does not go to concert,or it is not the case that he does not read book and does not play football.

P:Gonzolo play music , Q: Gonzolo go to concert , R:Gonzolo reads book ,S: Gonzolo play football.

When i try to translate it into symbolic logic, i confused in "it is not the case that". I am hesitating between two translation .Which one is correct?

the first : (∼P∧∼Q)∨(R∧∼S)

the second :∼(P∧∼Q)∨∼(∼R∧∼S)

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  • The second is the correct one.
    – lemontree
    Aug 22 '20 at 13:38
  • @lemontree i was thinking that the first one is correct because "it is not the case that" does not come before a connective, it comes before a sentence.Can you enlighten me
    – Bulbasaur
    Aug 22 '20 at 13:41
  • It does come before a sentence -- namely before the first subsentence, P ^ ~Q.
    – lemontree
    Aug 22 '20 at 13:42
  • @lemontree how did you conclude it ? there is not any comma after "it is not the case that"
    – Bulbasaur
    Aug 22 '20 at 13:43
  • Why would there be a comma after "it is not the case that"? "It is not the case that" technically means the same as "not", but is more often used to negate a complex sentence, while "not" is usually understood to negate the immediately following proposition. This makes it more likely that the English sentence intends the first "it is not the case that" to apply to P ^ ~Q, rather than P. Besides, there are two negations missing on the second subsentence in your first solution.
    – lemontree
    Aug 22 '20 at 13:50

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