can someone please check my work

Question

Given U ={all the letters of the alphabet}

A= {b,c,d} and B={c,e,f,g}

list the elements of set (A∪B')nB

{b,c,d,a}n{c}

Answer 1

(AUB')∩B

 

Apply the Distributive Law for set operations:

 

(AUB')∩B = A∩B U B'∩B

 

Now B'∩B = 0 (null), so:

 

(AUB')∩B = A∩B = {b, c, d}∩{c, e, f, g} = {c}