document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193411>Question 1193411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference A-B, of two sets A and B is defined to be the set of all<BR>\n" );
document.write( "elements in A that are ot in B. Use the Venn diagram to illustrate the<BR>\n" );
document.write( "following sets:<BR>\n" );
document.write( "(a)A − B(b)(A − B) ∩ (B − A),(c)(A ∪ B) − (A ∩ B)(c)U − A where<BR>\n" );
document.write( "U denote the universal set.<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 #825436 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=825436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Draw a rectangle to represent the universal set U<BR>\n" );
document.write( "Inside the rectangle, draw partially overlapping circles labeled A and B, as shown below<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"25%\" src = \"https://i.imgur.com/WP3dH8s.png\">\r<BR>\n" );
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document.write( "Part (a)<BR>\n" );
document.write( "The set A - B is where we shade the region inside A, but outside B. So it's the crescent shape moon highlighted in blue<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"25%\" src = \"https://i.imgur.com/LKvFXTR.png\"><BR>\n" );
document.write( "Effectively set A works like the universal set and we only focus on that. Then we further reduce/shrink things down by kicking out stuff found in set B.<BR>\n" );
document.write( "For more information, check out the concept of set complements.\r<BR>\n" );
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document.write( "Part (b)<BR>\n" );
document.write( "Refer to the previous part to see how A - B is set up<BR>\n" );
document.write( "Set B - A is a similar idea, but this time we shade the region marked in red<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"25%\" src = \"https://i.imgur.com/P2wDgS8.png\"><BR>\n" );
document.write( "Notice how the blue and red regions do NOT have anything in common. There's no overlap. <BR>\n" );
document.write( "Therefore (A − B) ∩ (B − A) will not have any shaded region and we will indicate this as an empty set.<BR>\n" );
document.write( "The drawing you should submit to your teacher should look like the very first venn diagram I posted above when I didn't shade anything. Be sure to tell your teacher that the empty set is involved. \r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "Unfortunately math tends to reuse a lot of symbols, or similarly looking symbols. The universal set U and the union symbol look very similar.\r<BR>\n" );
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document.write( "For the sake of clarity, I'll refer to the union symbol as the word \"union\"<BR>\n" );
document.write( "So instead of writing A U B, I'll write A union B\r<BR>\n" );
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document.write( "The set A union B is the set of things inside A, B, or both sets at once. <BR>\n" );
document.write( "We shade both circles and even the overlapped region between them to visually denote A union B<BR>\n" );
document.write( "If we kick out the set A ∩ B, then we end up with A-B on the left and B-A on the right. We union those two pieces together to end up with (A-B) union (B-A). \r<BR>\n" );
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document.write( "In other words,<BR>\n" );
document.write( "(A union B) - (A ∩ B) = (A-B) union (B-A)<BR>\n" );
document.write( "The drawing is exactly the same as mentioned in part (b) when I highlighted the blue set for A-B and the red set for B-A. Though I would use one single color to indicate that we're talking about one single set. The union of A-B with B-A is almost like we're gluing the two disjointed sets together, rather than trying to see what overlapped regions they have.\r<BR>\n" );
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document.write( "Part (d)\r<BR>\n" );
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document.write( "The set U - A is where we start with the entire universal set U, and then kick out stuff found in A. \r<BR>\n" );
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document.write( "Therefore, we shade the region outside of A as shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"25%\" src = \"https://i.imgur.com/VuhN6WS.png\"><BR>\n" );
document.write( "Be sure of course to stay inside the rectangle because we cannot get outside the universal set.\r<BR>\n" );
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document.write( "The notation U - A can be shortened to A' or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Ec ALIGN=MIDDLE  ALT=\"A%5Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" > to indicate the complement of set A, or the opposite of set A.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "A = set of all animals<BR>\n" );
document.write( "U-A = A' = set of all things that aren't an animal<BR>\n" );
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