I have read in quite a few books that the proposition 'p->q' can be read as either 'if p then q' and 'p only if q'.
Let p = it rains, and q = take an umbrella.
Then with according to the first form the argument is 'If it rains, take an umbrella'. And according to the second form the argument is 'Take an umbrella only if it rains'.
Then the cases 'it rains - took an umbrella (T)', 'it did not rain - did not took an umbrella (T)', 'it rains- did not took an umbrella (F)' are trivial.
But what about the case:
did not rain - took an umbrella.
Why is this true and not for example undefined or not known?