From the above question, you will clearly understand about weak Entity .
Let us revise what is weak Entity ?
1 . A weak entity is one which is depend upon other strong entity for its existence
2. The attributes in weak entity are not sufficient to identify tuples . so it need primary key of strong entity
3. If you have a relation of strong and weak entity . then the weak entity always have TOTAL participation . converse may not be true => every entity which has a total participation need not be a weak entity (check in the above figure )
4. you need to have an identifying relationship (double diamond box ) which happen to be in between PARTS and PRODUCTS and NOT between PARTS AND TRAINER
the above question check point no 3 and point no 4
Hence now it should be pretty clear that option a is true :)