AND, OR operators inside implications

Question

$$A \lor B \implies C$$

To prove this, is it sufficient to show that A implies C OR that B implies C?

This would seem most intuitive to me, but my lecture class today said that I would be required to show that A implies C AND that B implies C.

Answer 1

The following statements are equivalent: $$ (A \lor B) \implies C\\ \neg (A \lor B) \lor C\\ (\neg A \land \neg B) \lor C\\ (\neg A \lor C) \land (\neg B \lor C)\\ (A \implies C) \land (B \implies C)\\ $$