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  • If $\quad p \implies q\quad $ ($p$ implies $q$), then $p$ is a sufficient condition for $q$.

  • If $\quad \bar p \implies \bar q \quad$ (not $p$ implies not $q$), then $p$ is a necessary condition for $q$.

I don't understand what sufficient and necessary mean in this case. How do you know which one is necessary and which one is sufficient?

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    Those are the definitions of _necessary_ and of _sufficient_.2012-12-11
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    Are you aware that $\bar p \implies \bar q$ is the logical equivalent of $q \implies p$ ? Do you know what "necessary" and "sufficient" mean in the English language?2014-11-11

2 Answers 2