document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052740>Question 1052740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good morning ma'am/sir:<BR>\n" );
document.write( "I need your help for the following problems on quantification.<BR>\n" );
document.write( "Instructions: Let the universe of discourse in each case be the set of natural numbers.Determine the truth value. If true,prove it. If false,provide a counterexample.<BR>\n" );
document.write( "1. For all x there exist y such that (x < y)<BR>\n" );
document.write( "2. There exist x for all y such that (x < y)<BR>\n" );
document.write( "3. There exist x for some y such that (x < y).<BR>\n" );
document.write( "Please help me. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668088 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=668088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The natural numbers are 1, 2, 3, ...<BR>\n" );
document.write( "1. For all x there exist y such that (x < y) is TRUE,<BR>\n" );
document.write( "because y=x+1 is a natural number, and x<x+1 means x<y.<BR>\n" );
document.write( "2. There exist x for all y such that (x < y) is FALSE, because if Y=1, there is no natural number x such that x<1.<BR>\n" );
document.write( "3. There exist x for some y such that (x < y) is TRUE, because for all natural numbers y except y=1, there is x=1, such that x<y.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );