document.write( "Question 1196848: In a year group of 63 students, 22 study biology, 26 study Chemistry and 25 study Physics. 18 study both Physics and
\n" ); document.write( "Chemistry, four study Biology and Chemistry and three study both Physics and Biology. One studies all three subjects. How
\n" ); document.write( "many students study: \r
\n" ); document.write( "\n" ); document.write( "a) Biology only\r
\n" ); document.write( "\n" ); document.write( "b) Physics or Chemistry\r
\n" ); document.write( "\n" ); document.write( "c) None of Biology, Physics or Chemistry\r
\n" ); document.write( "\n" ); document.write( "d) Physics but not Chemistry? \n" ); document.write( "

Algebra.Com's Answer #829870 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In a year group of 63 students, 22 study biology, 26 study Chemistry and 25 study Physics.
\n" ); document.write( "18 study both Physics and Chemistry, four study Biology and Chemistry and three study both Physics and Biology.
\n" ); document.write( "One studies all three subjects.
\n" ); document.write( "How many students study:
\n" ); document.write( "a) Biology only
\n" ); document.write( "b) Physics or Chemistry
\n" ); document.write( "c) None of Biology, Physics or Chemistry
\n" ); document.write( "d) Physics but not Chemistry?
\n" ); document.write( "~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(a)  n(B_only) = n(B) - n(B ∩ C) - n(B ∩ P) + n(B ∩ C ∩ P) = 22 - 4 - 3 + 1 = 16.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  n(P U C) = n(P) + n(C) - n(P ∩ C) = 25 + 26 - 18 = 33.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c)  First calculate the union n(B U C U P) using the Inclusive-Exclusive principle formula\r\n" );
document.write( "\r\n" );
document.write( "         n(B U C U P) = n(B) + n(C) + n(P) - n(B ∩ C) - n(B ∩ P) - n(C ∩ P) + nn(B ∩ C ∩ P) = \r\n" );
document.write( "\r\n" );
document.write( "                      =  22  +  26  +  25  - 4  -  3  -  18  +   1 = 49.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Now the anwer to (c) is the complement of 49 to 63,  or  63-49 = 14.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(d)  n(P \ (P ∩ C) ) = n(P) - n(P ∩ C) = 25 - 18 = 7.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );