document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548454>Question 548454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8. Determine which, if any, of the three statements are equivalent. Show steps. Give a reason for your conclusion. Show complete work and submit your solution to the Dropbox.  <BR>\n" );
document.write( "1) if it is sunny, then I will go swimming<BR>\n" );
document.write( "2) If i do not go swimming, then it is not sunny.<BR>\n" );
document.write( "3) Either it is sunny or I will go swimming.\r<BR>\n" );
document.write( "\n" );
document.write( "a)1,2,and 3 are equivalent<BR>\n" );
document.write( "b)1 and 2 are equivalent<BR>\n" );
document.write( "c)2 and 3 are equivalent<BR>\n" );
document.write( "d)1 and 3 are equivalent<BR>\n" );
document.write( "e) none are equivalent </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357164 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=357164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The drop box! I thought I had seen the last of it when my son graduated from Connections Academy.<BR>\n" );
document.write( "It is obvious to me that 1 and 2 are equivalent. Statement 3 is not equivalent to them. So the right answer is b).<BR>\n" );
document.write( "How to prove it to your teacher's content is another story.<BR>\n" );
document.write( "Your lessons or textbook must give you the right format for your proof.<BR>\n" );
document.write( "A=it's sunny<BR>\n" );
document.write( "B=I go swimming.<BR>\n" );
document.write( "Statement 1 says If A, then B.<BR>\n" );
document.write( "Statement 2 says If not B, then not A. That is the contrapositive of statement 1, and they are both equivalent.<BR>\n" );
document.write( "Statement 3 says Either A or B is true, which I take to imply that both cannot be true at the same time.<BR>\n" );
document.write( "They may have taught you ways to express the statements and symbols to abbreviate<BR>\n" );
document.write( "the \"If ...,then ...\" relationship and the \"not\" in the statements.<BR>\n" );
document.write( "They would have told you that a statement implies its contrapositive. If one is true, so is the other.<BR>\n" );
document.write( "Alternatively you could have been told to use diagrams to express relationships. <BR>\n" );
document.write( "If A, then B can be represented as<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C0%2C10%2C0%2C10%2C%0D%0Acircle%285%2C5%2C4%29%2Ccircle+%284%2C4%2C2%29%2C%0D%0Alocate%284%2C+4%2CA%29%2C+locate%287.83%2C+8.5%2CB%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The inner circle would represents \"A is true\" (It's sunny).<BR>\n" );
document.write( "Every point in that circle is certainly in circle B.<BR>\n" );
document.write( "The large circle,B , represent \"B is true\" (I go swimming).<BR>\n" );
document.write( "I may go swimming when it's not sunny, so those cases would be in the part of circle B that is not inside circle A.<BR>\n" );
document.write( "You can graphically see that if not B (if you are outside circle B), not A (you are outside of circle A too.<BR>\n" );
document.write( "Either A or B (but not both) , meaning \"Either it is sunny or I will go swimming.\" would be represented by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C0%2C10%2C0%2C10%2C%0D%0Acircle%287%2C7%2C2.5%29%2Ccircle+%282.5%2C2.5%2C2.3%29%2C%0D%0Alocate%288%2C8%2CA%29%2C+locate%282%2C2%2CB%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >You cannot be in both circles at the same time. </SPAN>\n" );
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