document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040391>Question 1040391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can I please have your assistance? Let D be the set of all calendar dates from 4/30/1789 to 9/25/2014? Let P be the set of names of U.S. presidents. Let F be the set of names of first ladies of the U.S. Consider the following two functions pres: D arrow P where pres (d) is the name of the president of the U.S on the date d (the incumbent on inauguration days, to avoid ambiguity) and lady: P arrow F where lady (p) is the name of the first lady of the U.S. during the presidency of president p. Question: Can the composition pres o lady be defined? What about lady o pres? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655320 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The composition pres o lady cannot be defined, since the value of the function lady has the name of a first lady as a function value, but the function pres has the dates of presidential inauguration as domain values.\r<BR>\n" );
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document.write( "The composition lady o pres CAN be defined.  The function pres has range values from P, which can be substituted into the function lady.  <BR>\n" );
document.write( "Symbolically, \r<BR>\n" );
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document.write( "D-->P-->F, \r<BR>\n" );
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document.write( "or the composition would bring D into P into F. </SPAN>\n" );
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