I would like to ask a question about the usage of relative adverb
I know that sometimes we can use "when", "where" and "why" instead of relative pronoun + preposition to make a sentence less formal.
For example,
1) This is the park where we played.
2) Tuesday is the day when we have pizza for dinner.
3) Our teacher told us the reason why we study grammar.
However, I've seen some similar sentences which contain no "the park", "the day" and "the reason"
a) This is where we played.
b) Tuesday is when we have pizza for dinner.
c) Our teacher told us why we study grammar.
I wish to know which expression is correct. My teacher taught me that "where we played" is an adjectival clause to modify its antecedent "the park" and "why we study grammar" modifies "the reason"
Does it mean the example above a, b, c are incorrect. But I really read them on newspaper a lot.
Thanks in advance.