What is a good equivalent statement to : If the garden is not watered every day, the flowers wilt. Using the Morgan's Laws
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2$\begingroup$ Let $A$ denote "the garden is watered every day" and $B$ denote "the flowers wilt". Your statement is $(\neg A) \Rightarrow B$, which you can also write as $A \vee B$. Apply De Morgan as you wish. $\endgroup$– Clive NewsteadMay 23, 2012 at 18:16
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1 Answer
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And one equivalent statement is the contrapositive. Note that this isn't the same thing as a negative. The contrapositive of your statement is:
If the flowers haven't wilted, the garden has been watered every day.
Note that in both cases, some things are unspecified. What happens when the garden is watered everyday? Can the flowers still wilt when watered? The beautiful thing is that the parts left unanswered are also the same in the contrapositive, so this isn't a problem. In general, if you have
A implies B
then
not(B) implies not(A)
is the contrapositive, and is always true iff the original statement is true.
answered May 23, 2012 at 18:07