You're right.
With this you can conclude.Work:
~ ( ~ P OR Q ) is F
Is this true or false if P is false and Q is true
~ ( ~ P OR Q ) AND ( ~ P OR ~ ( P AND ~ Q ) )
Work:
~ ( ~ P OR Q ) is F
~ ( P AND ~ Q ) is T
( ~ P OR ~ ( P AND ~ Q ) ) is T
~ ( ~ P OR Q ) AND ( ~ P OR ~ ( P AND ~ Q ) ) is False