document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029233>Question 1029233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A is an event, and Ac is the complement of A. <BR>\n" );
document.write( "Which of the following statements are true?  Please show work.\r<BR>\n" );
document.write( "\n" );
document.write( "(a) P(A AND A^C)=1<BR>\n" );
document.write( "(b) P(A AND A^C = 0<BR>\n" );
document.write( "© P(A OR A^C)=1<BR>\n" );
document.write( "(d) P(A OR A^C) = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644507 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(A_or_B)=P(A)+P(B)-P(A_and_B)<BR>\n" );
document.write( "So for complements,<BR>\n" );
document.write( "P(A_or_Ac)=P(A)+P(Ac)-P(A_and_Ac)<BR>\n" );
document.write( "However by definition of complement,<BR>\n" );
document.write( "P(A_and_Ac)=0<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "P(A_or_Ac)=P(A)+P(Ac)<BR>\n" );
document.write( "P(A_or_Ac)=1<BR>\n" );
document.write( "So for example, probability that it will rain or that it won't rain is 100%. _ </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );