document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194404>Question 1194404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey of 130 pet owners yielded the following information: 47 own fish; 53 own a bird; 50 own a cat; 64 own a dog; 2 own all four; 11 own only fish; 14 own only a bird; 10 own fish and a bird; 21 own fish and a cat; 24 own a bird and a dog; 27 own a cat and a dog; 3 own fish, a bird, a cat, and no dog; 1 owns fish, a bird, a dog, and no cat; 9 own fish, a cat, a dog, and no bird; and 10 own a bird, a cat, a dog, and no fish. How many of the surveyed pet owners have no fish, no birds, no cats, and no dogs? (They own other types of pets.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826612 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "A = person owns a fish<BR>\n" );
document.write( "B = person owns a bird<BR>\n" );
document.write( "C = person owns a cat<BR>\n" );
document.write( "D = person owns a dog\r<BR>\n" );
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document.write( "There are 4 pets, so there are 2^4 = 16 different possibilities.\r<BR>\n" );
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document.write( "Here are the 16 possibilities<ol><li>Person doesn't own any of the four pets mentioned</li><li>A - persons owns a fish only</li><li>B - they own a bird only</li><li>C - owns a cat only </li><li>D - owns a dog only</li><li>AB - fish and bird only</li><li>AC - fish and cat only</li><li>AD - fish and dog only</li><li>BC - bird and cat only</li><li>BD - bird and dog only</li><li>CD - cat and dog only</li><li>BCD - bird, cat, and dog (i.e. everything but a fish)</li><li>ACD - fish, cat and dog (i.e. everything but a bird)</li><li>ABD - fish, bird and dog (everything but a cat)</li><li>ABC - fish, bird and cat (everything but a dog)</li><li>ABCD - person owns all four pets mentioned</li></ol><BR>\n" );
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document.write( "<BR>\n" );
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document.write( "Let's draw out the Venn Diagram.\r<BR>\n" );
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document.write( "Start by drawing two ovals like so. Make sure they overlap.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/5t7uRoN.png\"><BR>\n" );
document.write( "Create a mirror copy of those two ovals to have a total of four ovals.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width = \"45%\" src = \"https://i.imgur.com/KR11SNu.png\"><BR>\n" );
document.write( "Then slide the ovals over until we get this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width = \"45%\" src = \"https://i.imgur.com/KOPAE27.png\"><BR>\n" );
document.write( "It may seem like a bit of a mess, so be sure you can break apart the various ovals (or be able to spot the four ovals). <BR>\n" );
document.write( "This is why I recommend following these steps to slide the ovals over.<BR>\n" );
document.write( "Unfortunately we can't have the ovals separated or else we won't be able to form the overlapped regions needed.\r<BR>\n" );
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document.write( "Next, we'll add the 15 labels mentioned in the previous section above. The first label of \"none of the 4 pets mentioned\" is ignored for now, as it goes outside the four ovals.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width = \"45%\" src = \"https://i.imgur.com/36IxHV8.png\"><BR>\n" );
document.write( "Color-coding things helps us separate the various regions (it may be easy to get lost)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width = \"45%\" src = \"https://i.imgur.com/RjpNNX0.png\"><BR>\n" );
document.write( "<ul><li>Regions in white are for the people who own exactly one pet only</li><li>Regions in blue are for the people who own exactly two pets only</li><li>Regions in red are for the people who own exactly three pets only</li><li>The region in green is for the people who own all four pets mentioned</li></ul>\r<BR>\n" );
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document.write( "Take note how something like region ABC is in ovals A, B and C at the same time. Region ABC is outside oval D.<BR>\n" );
document.write( "Similar logic applies to how the other regions are set up.<BR>\n" );
document.write( "The region outside the ovals represents people who own none of the four pets mentioned.\r<BR>\n" );
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document.write( "--------------------------------------------------------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Let's fill out the Venn Diagram with numeric values.\r<BR>\n" );
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document.write( "To do so, we'll need to use the given facts:<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Number</TD><TD >Statement</TD></tr><tr><TD ><font color=blue>1</font></TD><TD >47 own fish</TD></tr><tr><TD ><font color=blue>2</font></TD><TD >53 own a bird</TD></tr><tr><TD ><font color=blue>3</font></TD><TD >50 own a cat</TD></tr><tr><TD ><font color=blue>4</font></TD><TD >64 own a dog</TD></tr><tr><TD ><font color=blue>5</font></TD><TD >2 own all four</TD></tr><tr><TD ><font color=blue>6</font></TD><TD >11 own only fish</TD></tr><tr><TD ><font color=blue>7</font></TD><TD >14 own only a bird</TD></tr><tr><TD ><font color=blue>8</font></TD><TD >10 own fish and a bird</TD></tr><tr><TD ><font color=blue>9</font></TD><TD >21 own fish and a cat</TD></tr><tr><TD ><font color=blue>10</font></TD><TD >24 own a bird and a dog</TD></tr><tr><TD ><font color=blue>11</font></TD><TD >27 own a cat and a dog</TD></tr><tr><TD ><font color=blue>12</font></TD><TD >3 own fish, a bird, a cat, and no dog</TD></tr><tr><TD ><font color=blue>13</font></TD><TD >1 owns fish, a bird, a dog, and no cat</TD></tr><tr><TD ><font color=blue>14</font></TD><TD >9 own fish, a cat, a dog, and no bird</TD></tr><tr><TD ><font color=blue>15</font></TD><TD >10 own a bird, a cat, a dog, and no fish</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "We start with statement 5, which says \"2 own all four\"<BR>\n" );
document.write( "This number goes inside the region labeled ABCD.<BR>\n" );
document.write( "In other words, this number goes in the region that is inside all four ovals.\r<BR>\n" );
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document.write( "Now move onto statement 6. It says \"11 own only fish\", which means 11 goes in the region labeled \"A\". <BR>\n" );
document.write( "This is the region inside oval A, but outside any other oval.\r<BR>\n" );
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document.write( "\n" );
document.write( "Now onto statement 7. It says \"14 own only a bird\", so we'll write \"14\" in region B. This is the region inside oval B, but outside any other oval.\r<BR>\n" );
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document.write( "Let's jump ahead to statement 12.<BR>\n" );
document.write( "It says \"3 own fish, a bird, a cat, and no dog\".<BR>\n" );
document.write( "We'll write the number 3 inside the region labeled \"ABC\". <BR>\n" );
document.write( "This is the region inside ovals A,B,C but outside oval D.<BR>\n" );
document.write( "To be more accurate, I'll write it off to the side since region ABC is very small.<BR>\n" );
document.write( "I'll be doing the same with regions ABD, AC and BD as well.\r<BR>\n" );
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document.write( "The next statement (statement 13) says \"1 owns fish, a bird, a dog, and no cat\"<BR>\n" );
document.write( "The number \"1\" goes with region ABD.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Up next is the statement \"9 own fish, a cat, a dog, and no bird\" (statement 14). It tells us that the number 9 goes inside region ACD.\r<BR>\n" );
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document.write( "Up next is the statement \"10 own a bird, a cat, a dog, and no fish\" (statement 15). <BR>\n" );
document.write( "It tells us that the number 10 goes inside region BCD.\r<BR>\n" );
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document.write( "Here's a mini recap so far:<BR>\n" );
document.write( "A = 11<BR>\n" );
document.write( "B = 14<BR>\n" );
document.write( "ABC = 3<BR>\n" );
document.write( "ABD = 1<BR>\n" );
document.write( "ACD = 9<BR>\n" );
document.write( "BCD = 10<BR>\n" );
document.write( "ABCD = 2<BR>\n" );
document.write( "That takes care of 7 regions, so there are 16-7 = 9 more to go.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "This is what your Venn Diagram should look like at this point (after filling in the proper regions)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width = \"45%\" src = \"https://i.imgur.com/aSbbeiD.png\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We'll move to statement 8 now.<BR>\n" );
document.write( "It says \"10 own fish and a bird\"<BR>\n" );
document.write( "Use a pen tool to highlight oval A and oval B as shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width = \"45%\" src = \"https://i.imgur.com/xkWAjHL.png\"><BR>\n" );
document.write( "The two ovals highlighted overlap in this teardrop shaped region marked below<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width = \"45%\" src = \"https://i.imgur.com/V68B5CJ.png\"><BR>\n" );
document.write( "Everything in this teardrop region is in oval A and oval B at the same time. The subregions involved in this teardrop are:<BR>\n" );
document.write( "Region AB<BR>\n" );
document.write( "Region ABC<BR>\n" );
document.write( "Region ABD<BR>\n" );
document.write( "Region ABCD<BR>\n" );
document.write( "Each of the four strings starts with \"AB\", and we either leave it as is, or we tack on various combos of C and/or D.<BR>\n" );
document.write( "This is a methodical way to list out all the possibilities of someone owning a fish and a bird (and possibly a cat and/or dog).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Algebraically we can form the equation<BR>\n" );
document.write( "AB+ABC+ABD+ABCD = 10<BR>\n" );
document.write( "since 10 people own a fish and a bird (and possibly a cat and/or dog).\r<BR>\n" );
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document.write( "\n" );
document.write( "Be careful and try not to think about something like \"ABC\" as \"A*B*C\".<BR>\n" );
document.write( "ABC is one variable name, and not the product of three separate variables.\r<BR>\n" );
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document.write( "\n" );
document.write( "We'll apply the following substitutions<BR>\n" );
document.write( "ABC = 3<BR>\n" );
document.write( "ABD = 1<BR>\n" );
document.write( "ABCD = 2<BR>\n" );
document.write( "to go from this<BR>\n" );
document.write( "AB+ABC+ABD+ABCD = 10<BR>\n" );
document.write( "to this<BR>\n" );
document.write( "AB+3+1+2 = 10<BR>\n" );
document.write( "and it solves to <BR>\n" );
document.write( "AB = 4<BR>\n" );
document.write( "This says \"4 people have a fish and a bird, but not a cat and not a dog\".<BR>\n" );
document.write( "That was all for statement 8. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now onto statement 9.<BR>\n" );
document.write( "We'll have this equation<BR>\n" );
document.write( "AC+ABC+ACD+ABCD = 21<BR>\n" );
document.write( "Each item on the left hand side has \"A\" and \"C\" in it somewhere.<BR>\n" );
document.write( "Plug in these items<BR>\n" );
document.write( "ABC = 3<BR>\n" );
document.write( "ACD = 9<BR>\n" );
document.write( "ABCD = 2<BR>\n" );
document.write( "to go from this<BR>\n" );
document.write( "AC+ABC+ACD+ABCD = 21<BR>\n" );
document.write( "to this<BR>\n" );
document.write( "AC+3+9+2 = 21<BR>\n" );
document.write( "which solves to <BR>\n" );
document.write( "AC = 7<BR>\n" );
document.write( "Therefore, 7 people have a fish and a cat, but none of the other two mentioned pets.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Onto statement 10.<BR>\n" );
document.write( "We'll have this equation<BR>\n" );
document.write( "BD+ABD+BCD+ABCD = 24<BR>\n" );
document.write( "Each item on the left hand side has \"B\" and \"D\" in it somewhere.<BR>\n" );
document.write( "Plug in these items<BR>\n" );
document.write( "ABD = 1<BR>\n" );
document.write( "BCD = 10<BR>\n" );
document.write( "ABCD = 2<BR>\n" );
document.write( "to go from this<BR>\n" );
document.write( "BD+ABD+BCD+ABCD = 24<BR>\n" );
document.write( "to this<BR>\n" );
document.write( "BD+1+10+2 = 24<BR>\n" );
document.write( "which solves to <BR>\n" );
document.write( "BD = 11<BR>\n" );
document.write( "Therefore, 11 people have a bird and a dog, but none of the other two mentioned pets.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Onto statement 11.<BR>\n" );
document.write( "We'll have this equation<BR>\n" );
document.write( "CD+ACD+BCD+ABCD = 27<BR>\n" );
document.write( "Each item on the left hand side has \"CD\" in it.<BR>\n" );
document.write( "Plug in these items<BR>\n" );
document.write( "ACD = 9<BR>\n" );
document.write( "BCD = 10<BR>\n" );
document.write( "ABCD = 2<BR>\n" );
document.write( "to go from this<BR>\n" );
document.write( "CD+ACD+BCD+ABCD = 27<BR>\n" );
document.write( "to this<BR>\n" );
document.write( "CD+9+10+2 = 27<BR>\n" );
document.write( "which solves to <BR>\n" );
document.write( "CD = 6<BR>\n" );
document.write( "Therefore, 6 people have a cat and a dog, but none of the other two mentioned pets.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's update that previous recap:<BR>\n" );
document.write( "ABCD = 2<BR>\n" );
document.write( "A = 11<BR>\n" );
document.write( "B = 14<BR>\n" );
document.write( "ABC = 3<BR>\n" );
document.write( "ABD = 1<BR>\n" );
document.write( "ACD = 9<BR>\n" );
document.write( "BCD = 10<BR>\n" );
document.write( "<font color=red>AB = 4<BR>\n" );
document.write( "AC = 7<BR>\n" );
document.write( "BD = 11<BR>\n" );
document.write( "CD = 6</font><BR>\n" );
document.write( "The new items are in red.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "--------------------------------------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Go back to the top to statement 1.<BR>\n" );
document.write( "47 people own a fish. Some of these 47 people own a fish only, while others may own exactly one other pet along with the fish, or two other pets along with the fish, or own all 4 pets mentioned.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A = fish owners only<BR>\n" );
document.write( "AB = fish + bird<BR>\n" );
document.write( "AC = fish + cat<BR>\n" );
document.write( "AD = fish + dog<BR>\n" );
document.write( "ABC = fish + bird + cat<BR>\n" );
document.write( "ABD = fish + bird + dog<BR>\n" );
document.write( "ACD = fish + cat + dog<BR>\n" );
document.write( "ABCD = all four pets mentioned<BR>\n" );
document.write( "It may help to use your pen tool to circle all of oval A.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have the following values:<BR>\n" );
document.write( "A = 11 (given from statement 6)<BR>\n" );
document.write( "AB = 4 (solved earlier; see statement 8)<BR>\n" );
document.write( "AC = 7 (solved earlier; see statement 9)<BR>\n" );
document.write( "AD = unknown, we'll be solving for it soon<BR>\n" );
document.write( "ABC = 3 (solved earlier; see statement 12)<BR>\n" );
document.write( "ABD = 1 (solved earlier; see statement 13)<BR>\n" );
document.write( "ACD = 9 (solved earlier; see statement 14)<BR>\n" );
document.write( "ABCD = 2 (given; see statement 5)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These values must add up to the 47 fish owners<BR>\n" );
document.write( "A+AB+AC+AD+ABC+ABD+ACD+ABCD = 47<BR>\n" );
document.write( "11+4+7+AD+3+1+9+2 = 47<BR>\n" );
document.write( "AD+37 = 47<BR>\n" );
document.write( "AD = 47-37<BR>\n" );
document.write( "AD = 10<BR>\n" );
document.write( "There are 10 people who have a fish and a dog, but no other pet mentioned.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Move onto statement 2, which says \"53 own a bird\".<BR>\n" );
document.write( "We'll circle the regions that involve the letter B in some fashion, i.e. we'll circle all of oval B.<BR>\n" );
document.write( "B = bird owners only<BR>\n" );
document.write( "AB = fish + bird<BR>\n" );
document.write( "BC = bird + cat<BR>\n" );
document.write( "BD = bird + dog<BR>\n" );
document.write( "ABC = fish + bird + cat<BR>\n" );
document.write( "ABD = fish + bird + dog<BR>\n" );
document.write( "BCD = bird + cat + dog<BR>\n" );
document.write( "ABCD = all four pets mentioned\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We'll be using these values to help solve for variable BC<BR>\n" );
document.write( "B = 14 (given; see statement 7)<BR>\n" );
document.write( "AB = 4 (solved earlier; see statement 8)<BR>\n" );
document.write( "BD = 11 (solved earlier; see statement 10)<BR>\n" );
document.write( "ABC = 3 (solved earlier; see statement 12)<BR>\n" );
document.write( "ABD = 1 (solved earlier; see statement 13)<BR>\n" );
document.write( "BCD = 10 (solved earlier; see statement 15)<BR>\n" );
document.write( "ABCD = 2 (given; see statement 5)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So,<BR>\n" );
document.write( "B+AB+BC+BD+ABC+ABD+BCD+ABCD = 53<BR>\n" );
document.write( "14+4+BC+11+3+1+10+2 = 53<BR>\n" );
document.write( "BC = 8<BR>\n" );
document.write( "There are 8 pet owners that have a bird and a cat, but no other pets mentioned.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now onto statement 3.<BR>\n" );
document.write( "Circle oval C, i.e. circle each region that involves C in some way<BR>\n" );
document.write( "C = cat only<BR>\n" );
document.write( "AC = fish and cat only<BR>\n" );
document.write( "BC = bird and cat only<BR>\n" );
document.write( "CD = cat and dog only<BR>\n" );
document.write( "ABC = fish + bird + cat<BR>\n" );
document.write( "ACD = fish + cat + dog<BR>\n" );
document.write( "BCD = bird + cat + dog<BR>\n" );
document.write( "ABCD = all four pets mentioned\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have the following values:<BR>\n" );
document.write( "AC = 7 (solved earlier in statement 9)<BR>\n" );
document.write( "BC = 8 (solved earlier in statement 2)<BR>\n" );
document.write( "CD = 6 (solved earlier in statement 11)<BR>\n" );
document.write( "ABC = 3 (see statement 12)<BR>\n" );
document.write( "ACD = 9 (see statement 14)<BR>\n" );
document.write( "BCD = 10 (see statement 15)<BR>\n" );
document.write( "ABCD = 2 (see statement 5)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So,<BR>\n" );
document.write( "C+AC+BC+CD+ABC+ACD+BCD+ABCD = 50<BR>\n" );
document.write( "C+7+8+6+3+9+10+2 = 50<BR>\n" );
document.write( "C+45 = 50<BR>\n" );
document.write( "C = 50-45<BR>\n" );
document.write( "C = 5<BR>\n" );
document.write( "There are 5 people who own a cat only (and none of the other three pets mentioned).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now onto the last statement left, which is statement 4.<BR>\n" );
document.write( "There are 64 people who own a dog which means,<BR>\n" );
document.write( "D+AD+BD+CD+ABD+ACD+BCD+ABCD = 64<BR>\n" );
document.write( "D+10+11+6+1+9+10+2 = 64<BR>\n" );
document.write( "D+49 = 64<BR>\n" );
document.write( "D = 64-49<BR>\n" );
document.write( "D = 15<BR>\n" );
document.write( "There are 15 dog owners who do not have a fish, nor a bird, nor a cat.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's the complete summary of what we found<BR>\n" );
document.write( "A = 11<BR>\n" );
document.write( "B = 14<BR>\n" );
document.write( "C = 5<BR>\n" );
document.write( "D = 15<BR>\n" );
document.write( "AB = 4<BR>\n" );
document.write( "AC = 7<BR>\n" );
document.write( "AD = 10<BR>\n" );
document.write( "BC = 8<BR>\n" );
document.write( "BD = 11<BR>\n" );
document.write( "CD = 6<BR>\n" );
document.write( "ABC = 3<BR>\n" );
document.write( "ABD = 1<BR>\n" );
document.write( "ACD = 9<BR>\n" );
document.write( "BCD = 10<BR>\n" );
document.write( "ABCD = 2<BR>\n" );
document.write( "This is what the completed Venn Diagram looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width = \"45%\" src = \"https://i.imgur.com/G9NXBdh.png\"><BR>\n" );
document.write( "The 14 outside of all of the ovals is the final answer and explained in the next two paragraphs.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add up all of those values to find out how many people there are that own at least one of the four pets mentioned.<BR>\n" );
document.write( "A+B+C+D+AB+AC+AD+BC+BD+CD+ABC+ABD+ACD+BCD+ABCD<BR>\n" );
document.write( "11+14+5+15+4+7+10+8+11+6+3+1+9+10+2<BR>\n" );
document.write( "116\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 116 people who have at least one pet of the four pets mentioned.<BR>\n" );
document.write( "There are 130 people total. <BR>\n" );
document.write( "That must mean there are 130-116 = 14 people who do not have any of the four pets mentioned.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Final Answer: <font color=red>14</font><BR>\n" );
document.write( "</font><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );