document.write( "Question 1201448: Let A and B be subsets of a universal set U and suppose n(U) = 200, n(A) = 100, n(B) = 80, and n(A ∩ B) = 40. Compute:
\n" ); document.write( " n(A ∪ B)
\n" ); document.write( " n(Ac)
\n" ); document.write( " n(A ∩ Bc) \n" ); document.write( "

Algebra.Com's Answer #835826 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Let A and B be subsets of a universal set U and suppose n(U) = 200, n(A) = 100, n(B) = 80, and n(A ∩ B) = 40. Compute:
\n" ); document.write( "(a) n(A ∪ B)
\n" ); document.write( "(b) n(Ac)
\n" ); document.write( "(c) n(A ∩ Bc)
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(a)  n(A U B) = n(A) + n(B) - n(A ∩ B) = 100 + 80 - 40 = 140.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  n(A^c) = n(U) - n(A) = 200 - 100 = 100.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c)  The set  A ∩ B^c  consists of those elements from A that do not belong to B.\r\n" );
document.write( "\r\n" );
document.write( "     In other words,  A ∩ Bc = A \ (A ∩ B).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     THEREFORE,  n(A ∩ B^c) = n(A) - n(A ∩ B) = 100 - 40 = 60.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I answered all your questions.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );