document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176925>Question 1176925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Choose the best answer..\r<BR>\n" );
document.write( "\n" );
document.write( "1.) Which statement has the same truth value in the statement,<BR>\n" );
document.write( "“If the number is even, then it is divisible by two”?<BR>\n" );
document.write( "a. If the number is divisible by two, then it is even.<BR>\n" );
document.write( "b. If the number is not even, then it is not divisible by two.<BR>\n" );
document.write( "c. If the number is not divisible by two, then it is not even.<BR>\n" );
document.write( "2.) Given the statement, “If a polygon is pentagon, then it has five<BR>\n" );
document.write( "sides”, what is the contrapositive?<BR>\n" );
document.write( "a. If a polygon has five sides, then it is a pentagon.<BR>\n" );
document.write( "b. If a polygon is not pentagon, then it has no five sides.<BR>\n" );
document.write( "c. If a polygon has no five sides, then it is not a pentagon.\r<BR>\n" );
document.write( "\n" );
document.write( "For items 3 -5, if p: A = πr2 and q: r = 10<BR>\n" );
document.write( "3.) What statement is equivalent to q → p?<BR>\n" );
document.write( "a. If r = 10, then A = πr2<BR>\n" );
document.write( "b. If A ≠ πr2, then r ≠ 10<BR>\n" );
document.write( "c. If r ≠ 10, then A ≠ πr2<BR>\n" );
document.write( "4.) What statement is equivalent to ~q → ~p?<BR>\n" );
document.write( "a. If r = 10, then A = πr2<BR>\n" );
document.write( "b. If A ≠ πr2, then r ≠ 10<BR>\n" );
document.write( "c. If r ≠ 10, then A ≠ πr2<BR>\n" );
document.write( " 5.) What statement is equivalent to ~p → ~q?<BR>\n" );
document.write( "a. If r = 10, then A = πr2<BR>\n" );
document.write( "b. If A ≠ πr2, then r ≠ 10<BR>\n" );
document.write( "c. If r ≠ 10, then A ≠ πr2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850548 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down each question:\r<BR>\n" );
document.write( "\n" );
document.write( "**1.) Which statement has the same truth value in the statement, “If the number is even, then it is divisible by two”?**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Original statement:** If P, then Q (P: number is even, Q: number is divisible by two)<BR>\n" );
document.write( "* We're looking for the **converse**, **inverse**, or **contrapositive** that has the same truth value as the original statement.<BR>\n" );
document.write( "    * The converse (Q -> P) is: If the number is divisible by two, then it is even.<BR>\n" );
document.write( "    * The inverse (~P -> ~Q) is: If the number is not even, then it is not divisible by two.<BR>\n" );
document.write( "    * The contrapositive (~Q -> ~P) is: If the number is not divisible by two, then it is not even.\r<BR>\n" );
document.write( "\n" );
document.write( "* The original statement is true.<BR>\n" );
document.write( "* The converse is true.<BR>\n" );
document.write( "* The inverse is true.<BR>\n" );
document.write( "* The contrapositive is true.<BR>\n" );
document.write( "* The contrapositive always has the same truth value of the original statement.\r<BR>\n" );
document.write( "\n" );
document.write( "* **Answer: c. If the number is not divisible by two, then it is not even.**\r<BR>\n" );
document.write( "\n" );
document.write( "**2.) Given the statement, “If a polygon is pentagon, then it has five sides”, what is the contrapositive?**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Original statement:** If P, then Q (P: polygon is pentagon, Q: polygon has five sides)<BR>\n" );
document.write( "* **Contrapositive:** If ~Q, then ~P (If not Q, then not P)<BR>\n" );
document.write( "* **Answer: c. If a polygon has no five sides, then it is not a pentagon.**\r<BR>\n" );
document.write( "\n" );
document.write( "**For items 3 -5, if p: A = πr2 and q: r = 10**\r<BR>\n" );
document.write( "\n" );
document.write( "**3.) What statement is equivalent to q → p?**\r<BR>\n" );
document.write( "\n" );
document.write( "* **q → p:** If q, then p (If r = 10, then A = πr2)<BR>\n" );
document.write( "* **Answer: a. If r = 10, then A = πr2**\r<BR>\n" );
document.write( "\n" );
document.write( "**4.) What statement is equivalent to ~q → ~p?**\r<BR>\n" );
document.write( "\n" );
document.write( "* **~q → ~p:** If not q, then not p (If r ≠ 10, then A ≠ πr2)<BR>\n" );
document.write( "* **Answer: c. If r ≠ 10, then A ≠ πr2**\r<BR>\n" );
document.write( "\n" );
document.write( "**5.) What statement is equivalent to ~p → ~q?**\r<BR>\n" );
document.write( "\n" );
document.write( "* **~p → ~q:** If not p, then not q (If A ≠ πr2, then r ≠ 10)<BR>\n" );
document.write( "* **Answer: b. If A ≠ πr2, then r ≠ 10**<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );