document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190730>Question 1190730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MAT 145: Topics In Contemporary Math\r<BR>\n" );
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document.write( " Sets and Set Operations\r<BR>\n" );
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document.write( "Given the definitions for the sets, find the elements in the subsets in roster notation.\r<BR>\n" );
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document.write( "Universal set U is the set of all letters in the English alphabet, A is set of all full-time <BR>\n" );
document.write( "vowels (no y!), B is the set of the first 10 letters<BR>\n" );
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document.write( "A                   B                  𝐴 ∩ B\r<BR>\n" );
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document.write( "𝐴 ∪ B              A^c                  B^c\r<BR>\n" );
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document.write( "(𝐴 ∪ 𝐵)^c       (𝐴 ∩ 𝐵)^c         (𝐴 ∪ 𝐵) ∩ (𝐴 ∩ 𝐵)^c\r<BR>\n" );
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document.write( "𝐴 ∩ 𝐵^c      𝐴^c ∩ B                    𝐴 ∩ A^c </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822437 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=822437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "U = universal set = set of all letters from English alphabet<BR>\n" );
document.write( "U = {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}<BR>\n" );
document.write( "A = set of vowels (no y)<BR>\n" );
document.write( "A = {a,e,i,o,u}<BR>\n" );
document.write( "B = first 10 letters<BR>\n" );
document.write( "B = {a,b,c,d,e,f,g,h,i,j}<BR>\n" );
document.write( "note how A and B are subsets of the universal set.\r<BR>\n" );
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document.write( "The union of A and B is the collection of stuff from A or from B (or both)<BR>\n" );
document.write( "𝐴 ∪ B = {a,b,c,d,e,f,g,h,i,j,o,u}<BR>\n" );
document.write( "Notice how we only list one unique letter without any repeats. This means you'll toss out any duplicates.<BR>\n" );
document.write( "Sorting is optional but helpful.\r<BR>\n" );
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document.write( "The intersection of A and B is the set of what they have in common.<BR>\n" );
document.write( "𝐴 ∩ B = {a,e,i}\r<BR>\n" );
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document.write( "B^c = set of stuff that isn't in B<BR>\n" );
document.write( "B^c = {k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}<BR>\n" );
document.write( "In other words, it's the set of letters from k to z.\r<BR>\n" );
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document.write( "(𝐴 ∪ 𝐵)^c = set of stuff not in 𝐴 ∪ 𝐵<BR>\n" );
document.write( "(𝐴 ∪ 𝐵)^c = {k,l,m,n,p,q,r,s,t,v,w,x,y,z}<BR>\n" );
document.write( "basically we go from k to z but leave out the vowels o and u because they were found in 𝐴 ∪ B\r<BR>\n" );
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document.write( "I'll do one more but leave the rest for you to do<BR>\n" );
document.write( "(𝐴 ∩ 𝐵)^c = set of stuff not in 𝐴 ∩ 𝐵<BR>\n" );
document.write( "(𝐴 ∩ 𝐵)^c = {b,c,d,f,g,h,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}<BR>\n" );
document.write( "I started with the entire alphabet, then I kicked out letters a,e,i since they are found in 𝐴 ∩ 𝐵<BR>\n" );
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