Am I right?

1.   D  is correct.

2.   (P U R) ∩ Q

First let's find  P U R .

P U R   =   {red, blue, green, yellow, black, purple}

Now find the intersection of   P U R  and   Q

The intersection of  {red, blue, green, yellow, black, purple}  and  {red, green, black}

is   {red, green, black} .  So...

(P U R) ∩ Q   =   {red, green, black}

3.   C  is correct.