Question

Suppose that An B = {1, 4, 7, 8} and AU B = {1, 2, 3, 4, 5, 6, 7, 8, 9}. How many differentsets are possible for A?

Answer 1

From the information given;

$A\cap B=\mleft\lbrace1,4,7,8\mright\rbrace$

Knowing that this is a subset of A, then the elements of A must contain at least;

$A=\mleft\lbrace1,4,7,8\mright\rbrace$

Also, other possible elements of set A would be;

$\begin{gathered} A=\mleft\lbrace1,2,4,7,8\mright\rbrace \\ A=\mleft\lbrace1,2,3,4,7,8\mright\rbrace \\ A=\mleft\lbrace1,2,3,4,5,7,8\mright\rbrace \\ A=\mleft\lbrace1,2,3,4,5,6,7,8\mright\rbrace \\ A=\mleft\lbrace1,2,3,4,5,6,7,8,9\mright\rbrace \end{gathered}$

ANSWER:

There are six (6) different sets possible for A.