Are the following statement forms logically equivalent: p $$ q $->$ p and p $($ p $$ q$)?$

Question $4$ options:

They are logically equivalent, because they can produce the same output with the same inputs of p and q

They are not logically equivalent, because they always produce different outputs regardless of the inputs of p and q

They are logically equivalent, because they always produce the same output regardless of the inputs of p and q

They are not logically equivalent, because they can produce different outputs with the same inputs of p and q