Question

U={1,2,3,4,5,6,7,8}A={2,5,6}B={2,3,4,8}C={1,4,7} use the roster method AU(BUC)

Answer 1

The set BUC is a new set with the elements of set B and C:

$B\cup C=\mleft\lbrace1,2,3,4,7,8\mright\rbrace$

Now, AU(BUC) is the union of the elements in A and in BUC:

$A\cup(B\cup C)=\mleft\lbrace_{}1,2,3,4,5,6,7,8\mright\rbrace$