Answer
$(e \lor p) \leftrightarrow m.$
Work Step by Step
Our propositions are
m: "You can see the movie,"
e: "You are over 18 years old," and
p: "you have the permission of a parent."
We want to translate the statement "You can see the movie only if you are over 18 years old or you have the permission of a parent," into a logical proposition.
Notice that there is an implicit biconditional connective in our statement; the 'only if' should be 'if and only if'. Because what is meant by our statement is "If you are over 18 years old or you have the permission of a parent, then you can see the movie" and "If it is not the case that you are over 18 years old and it is not the case that you have the permission of a parent, then it is not the case that you can see the movie."
Notice also that that the 'or' in our statement is inclusive because if either or both of "You are over 18 years old," or "You have the permission of a parent " is true, then you can see the movie.
So a translation into propositional logic is $(e \lor p) \leftrightarrow m.$
