Assume A and B are regular sets, and C is another set $($not necessarily regular$).$ Let D$=($A $\backslash$cap B$)$C$.$ Check ALL the correct choices.

Question options:

If C is regular, then D is also regular.

If C is not regular, then D cannot be regular.

If C is regular, then D$=($AC $\backslash$cap BC$)$ always holds.

If C is regular, then D$=($AC $\backslash$cap BC$)$ never holds.

If C is not regular, then D$=($AC $\backslash$cap BC$)$ never holds.