document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196537>Question 1196537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let U = {q, r, s, t, u, v, w, x, y, z}, A = {q, s, u, w, y}, B = {q, s, y, z}, and C = {v, w, x, y, z}. List the elements in the following set.\r<BR>\n" );
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document.write( "A ∩ B with line on top </SPAN>\n" );
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document.write( "There's ambiguity when you mention \"with a line on top\"\r<BR>\n" );
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document.write( "Is the line solely over the B? Or is it over everything?\r<BR>\n" );
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document.write( "Do you mean <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A \cap \overline{B}\">\r<BR>\n" );
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document.write( "Or do you mean <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large  \overline{A \cap B}\">\r<BR>\n" );
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document.write( "I'll go over each interpretation.\r<BR>\n" );
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document.write( "Let's focus on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A \cap \overline{B}\">\r<BR>\n" );
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document.write( "The universal set is <BR>\n" );
document.write( "U = {q, r, s, t, u, v, w, x, y, z}<BR>\n" );
document.write( "Cross off the stuff you find in set B<BR>\n" );
document.write( "So we'll cross off: q, s, y, and z<BR>\n" );
document.write( "This forms the set B' which is the same as writing <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \overline{B}\"><BR>\n" );
document.write( "B' = {r, t, u, v, w, x}<BR>\n" );
document.write( "This is the complement of set B.\r<BR>\n" );
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document.write( "Stuff in B' is not found in B, and vice versa.<BR>\n" );
document.write( "They are complete opposite of one another.<BR>\n" );
document.write( "The two sets union together to form the universal set.\r<BR>\n" );
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document.write( "Think of it like this:<BR>\n" );
document.write( "stuff inside B is inside a house<BR>\n" );
document.write( "stuff outside B is outside the house\r<BR>\n" );
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document.write( "Now we'll intersect the set A with set B'<BR>\n" );
document.write( "A = {q, s, u, w, y}<BR>\n" );
document.write( "B' = {r, t, u, v, w, x}<BR>\n" );
document.write( "We see that the letters u and w are inside both A and B' at the same time. \r<BR>\n" );
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document.write( "Hence A ∩ B' = {u, w}<BR>\n" );
document.write( "which is the same as saying <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A \cap \overline{B} = \{ u, w \}\">\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "Now onto <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large  \overline{A \cap B}\">\r<BR>\n" );
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document.write( "This is the same as writing (A ∩ B)'<BR>\n" );
document.write( "We're taking the complement of set (A ∩ B)\r<BR>\n" );
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document.write( "Here are sets A and B<BR>\n" );
document.write( "A = {q, s, u, w, y}<BR>\n" );
document.write( "B = {q, s, y, z}<BR>\n" );
document.write( "which means,<BR>\n" );
document.write( "A ∩ B = {q, s, y}<BR>\n" );
document.write( "since those three letters are found in both sets\r<BR>\n" );
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document.write( "We'll delete q,s,y from the universal set<BR>\n" );
document.write( "U = {q, r, s, t, u, v, w, x, y, z}<BR>\n" );
document.write( "(A ∩ B)' = {<font color=red><s>q</s></font>, r, <font color=red><s>s</s></font>, t, u, v, w, x, <font color=red><s>y</s></font>, z}<BR>\n" );
document.write( "(A ∩ B)' = {r, t, u, v, w, x, z}\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large  \overline{A \cap B} = \{r, t, u, v, w, x, z\}\"><BR>\n" );
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document.write( " </SPAN>\n" );
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