ANSWER
[tex](A\cup B)\operatorname{\cap}C=\lbrace10,20\rbrace[/tex]
EXPLANATION
Set A contains multiples of 10 from 10 to 90:
[tex]A=\lbrace10,20,30,40,50,60,70,80,90\rbrace[/tex]
Set B contains multiples of 30 from 30 to 120:
[tex]B=\lbrace30,60,90,120\rbrace[/tex]
The union of two sets is the set that contains all the values in both sets. Therefore, A U B is:
[tex]A\cup B=\lbrace10,20,30,40,50,60,70,80,90,120\rbrace[/tex]
Set C contains even numbers from 2 to 20:
[tex]C=\lbrace2,4,6,8,10,12,14,16,18,20\rbrace[/tex]
The intersection of two sets is the set of values that exist in the two sets. Therefore, (A U B) n C is:
[tex](A\cup B)\cap C=\lbrace10,20\rbrace[/tex]
That is the answer.
