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P, Q, R, and S are four logical statements such that if P is true, then Q is true; if Q is true, then R is true; and if S is true, then at least one of Q and R is false. Then it follows that

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- if S is false, then both Q and R true
- if at least one of Q and R is true, then S is false
- if P is true, then S is false.
- if Q is true, then S is true.

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