document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190027>Question 1190027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Construct a truth table for each of the following.\r<BR>\n" );
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document.write( "3) (𝑝 ∧ 𝑞) 𝑉 𝑝\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821565 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=821565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The symbol ^ means \"and\". It refers to a logical conjunction. In logic textbooks, the symbol ^ does not mean exponent.\r<BR>\n" );
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document.write( "The symbol v means \"or\". It's a logical disjunction. \r<BR>\n" );
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document.write( "Here's a truth table for p ^ q<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >p</TD><TD >q</TD><TD >p ^ q</TD></tr><tr><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >T</TD><TD >F</TD><TD >F</TD></tr><tr><TD >F</TD><TD >T</TD><TD >F</TD></tr><tr><TD >F</TD><TD >F</TD><TD >F</TD></tr>\n" );
document.write( "</TABLE>T = true, F = false<BR>\n" );
document.write( "As the table shows, p ^ q is only true if BOTH p and q are true together. Otherwise, it's false.\r<BR>\n" );
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document.write( "Here's a table for p v q<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >p</TD><TD >q</TD><TD >p v q</TD></tr><tr><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >T</TD><TD >F</TD><TD >T</TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >F</TD><TD >F</TD></tr>\n" );
document.write( "</TABLE>We have the opposite situation going on here. <BR>\n" );
document.write( "The expression p v q is only false when BOTH p and q are false together. Otherwise, it's true.\r<BR>\n" );
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document.write( "Use the ideas mentioned to get<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >p</TD><TD >q</TD><TD >p ^ q</TD><TD >(p ^ q) v p</TD></tr><tr><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD></tr><tr><TD >F</TD><TD >T</TD><TD >F</TD><TD >F</TD></tr><tr><TD >F</TD><TD >F</TD><TD >F</TD><TD >F</TD></tr>\n" );
document.write( "</TABLE><font color=red>That table is the final answer.</font><BR>\n" );
document.write( "Notice how the final column is perfectly identical to the p column. <BR>\n" );
document.write( "Therefore, the expression (p ^ q) v p is logically equivalent to p.\r<BR>\n" );
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document.write( "If you wanted, you can have this as scratch work off to the side somewhere<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >p ^ q</TD><TD > p</TD><TD >(p ^ q) v p</TD></tr><tr><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >F</TD><TD >F</TD></tr><tr><TD >F</TD><TD >F</TD><TD >F</TD></tr>\n" );
document.write( "</TABLE>This way you can quickly compare this scratch work table to the p v q table shown earlier. <BR>\n" );
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