document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38180>Question 38180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey,80 computer science teachers were asked which of the three programming languages, Pascal, Fortran and C,have they used to introduce programming to students. Forty (40) teachers said they have used Pascal,35 said they have used Fortran, 25 said they have used C,20 said they have used both Pascal and Fortran,17 said they have used Pascal and C, 5 said they have used Fortran and C,and 3 said they have used all the three languages.\r<BR>\n" );
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document.write( "a)How many teachers have used Fortran alone?<BR>\n" );
document.write( "b)How many teachers have used both Pascal and C?<BR>\n" );
document.write( "c)How many teachers have used Fortran, but not C?<BR>\n" );
document.write( "d)How many used none of the three languages?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23831 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=23831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "  Given P = 40, F = 35, C = 25. <BR>\n" );
document.write( " P^F = 20, P^C = 17, F^C= 5, P^F^C = 3.<BR>\n" );
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document.write( " A diagram wiil be helpful.<BR>\n" );
document.write( " a) Use F alone: F - (F ^ P) - (F ^ C ) + P^F^C= 35 - 25 + 3 = 13.<BR>\n" );
document.write( " b) 17 use both P and C , P^C - P^F^C = 17 - 3 = 14 use P & C only<BR>\n" );
document.write( " c) F - F^C = 35 - 5 = 30\r<BR>\n" );
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document.write( " d)  The formula about inclusion-exclusion: (or Venn diagram)<BR>\n" );
document.write( " P U F U C = P + F + C - (P^F + P^C+ F^C) + P^F^C <BR>\n" );
document.write( "           = 40 + 60 - 42 + 3 = 61.\r<BR>\n" );
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document.write( " the complement (P U F U C )'  = 80 - 61 = 19... using none of three\r<BR>\n" );
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document.write( " khwang<BR>\n" );
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