## Identifying the necessary and sufficient conditions, Advanced Statistics

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You have probably noticed by now that some of the statements of necessary and sufficient conditions sound more natural than others. For example it seems more natural to express "We will go to the beach only if it is sunny" as "It being sunny is necessary for our going to the beach", than "Our going to the beach is sufficient for it being sunny". Although these are equivalent, the former sounds more like something we might actually say. When you are identifying the necessary and sufficient conditions here, make a note of which one sounds like it better captures the meaning of the sentence.

(i) If the wheat harvest fails, then Joe is going to sell the farm

(ii) People become angry if they are scared.

(iii) Only the lonely know what heartache is.

(iv) If we all spent more time asleep the murder rate would go down.

(v) The cat will bite if you pull her tail.

(vi) If you ask nicely, they will tell you.

(vii) If the ringleaders aren't found, the search will continue.

(viii) You open the door only if you know the person on the other side.

(ix) A swimmer can only become famous if she breaks records easily.

(xi) A swimmer is suspected of doping if she breaks records easily.

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