document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023326>Question 1023326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the venn diagram E is the set of all children in a certain chosen group, A={children in Youth Club A} and B={children in Youth club B}The letters p,q,x and y in the diagram represent the number of children in each subset.Given that n(E)=200, n(A)=75 and n(B)=35<BR>\n" );
document.write( "(i)find the smallest possible value of y where y is (AUB)' \r<BR>\n" );
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document.write( " (ii)the largest possible value of x where x is AnB.\r<BR>\n" );
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document.write( "(iii) find the value of of q if p= 45 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638836 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-4%2C4%2C-2%2C5%2Crectangle%28-4%2C-1.6%2C4%2C4.4%29%2Clocate%28-4%2C5%2CE%29%2Clocate%28-2%2C1.8%2Cp%29%2Clocate%281.5%2C1.7%2Cq%29%2Clocate%28-3.7%2C-1%2Cy%29%2C+locate%28-3.6%2C2.5%2CA%29%2C+locate%28-.1%2C1.8%2Cx%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C2%29%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C1.95%29%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C1.975%29%29%2C%0D%0Ablue%28circle%28sqrt%282%29%2Csqrt%282%29%2C2%29%2Ccircle%28sqrt%282%29%2Csqrt%282%29%2C1.95%29%2Ccircle%28sqrt%282%29%2Csqrt%282%29%2C1.975%29%29%2C%0D%0Alocate%283.4%2C2.5%2CB%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "N(A) = 75 = p+x<BR>\n" );
document.write( "N(B) = 35 = x+q<BR>\n" );
document.write( "n(E) = 200 = p+x+q+y\r<BR>\n" );
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document.write( "(i)find the smallest possible value of y where y is (AUB)' <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "That'll be when there's the most possible in the two circles,\r\n" );
document.write( "which is when their intersection x is the least, or when \r\n" );
document.write( "x=0, p=75, q=35, and y=90 (that's also when p and q are the\r\n" );
document.write( "most they can be, and x is the least it can be.)\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-4%2C4%2C-2%2C5%2Crectangle%28-4%2C-1.6%2C4%2C4.4%29%2Clocate%28-4%2C5%2CE%29%2C+locate%28-2%2C1.8%2Cp=75%29%2Clocate%281.5%2C1.7%2Cq=35%29%2Clocate%28-3.7%2C-1%2Cy=90%29%2C+locate%28-3.6%2C2.5%2CA%29%2C+locate%28-.4%2C1.8%2Cx=0%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C2%29%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C1.95%29%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C1.975%29%29%2C%0D%0Ablue%28circle%28sqrt%282%29%2Csqrt%282%29%2C2%29%2Ccircle%28sqrt%282%29%2Csqrt%282%29%2C1.95%29%2Ccircle%28sqrt%282%29%2Csqrt%282%29%2C1.975%29%29%2C%0D%0Alocate%283.4%2C2.5%2CB%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "(ii)the largest possible value of x where x is AnB. <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "That'll be when all of B is in x which is when q=0, \r\n" );
document.write( "x=35, p=40, and y=125.  (That's also when y is the most\r\n" );
document.write( "it can be, and when p and q are the least they can be) \r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-4%2C4%2C-2%2C5%2Crectangle%28-4%2C-1.6%2C4%2C4.4%29%2Clocate%28-4%2C5%2CE%29%2C+locate%28-2%2C1.8%2Cp=40%29%2Clocate%281.5%2C1.7%2Cq=0%29%2Clocate%28-3.7%2C-1%2Cy=125%29%2C+locate%28-3.6%2C2.5%2CA%29%2C+locate%28-.5%2C1.8%2Cx=35%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C2%29%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C1.95%29%29%2Cred%28circle%28-sqrt%282%29%2Csqrt%282%29%2C1.975%29%29%2C%0D%0Ablue%28circle%28sqrt%282%29%2Csqrt%282%29%2C2%29%2Ccircle%28sqrt%282%29%2Csqrt%282%29%2C1.95%29%2Ccircle%28sqrt%282%29%2Csqrt%282%29%2C1.975%29%29%2C%0D%0Alocate%283.4%2C2.5%2CB%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "(iii) find the value of of q if p= 45<BR>\n" );
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document.write( "That'll be when x=30, q=5, and y=120.\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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