document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164833>Question 1164833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following logical expression, place the operations in the order in which you would apply, from first operation to last.\r<BR>\n" );
document.write( "\n" );
document.write( "p → q ∨ ~r </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853510 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.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=853510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To determine the correct order of operations for the logical expression , we follow the standard rules of **operator precedence** in propositional logic.\r<BR>\n" );
document.write( "\n" );
document.write( "The general hierarchy of operations is:\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Parentheses** (None in this expression)<BR>\n" );
document.write( "2. **Negation** ( or )<BR>\n" );
document.write( "3. **Conjunction** () and **Disjunction** ()<BR>\n" );
document.write( "4. **Conditional** ()<BR>\n" );
document.write( "5. **Biconditional** ()\r<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
document.write( "\n" );
document.write( "### Order of Application\r<BR>\n" );
document.write( "\n" );
document.write( "Based on these rules, here is the order in which you would apply the operations for this expression:\r<BR>\n" );
document.write( "\n" );
document.write( "1. **First Operation: Negation ()**<BR>\n" );
document.write( "You must first find the truth value of \"not \" before it can be used in any other operation.<BR>\n" );
document.write( "2. **Second Operation: Disjunction ()**<BR>\n" );
document.write( "Following the hierarchy, the \"OR\" () operator is applied next. You take the result of  and combine it with .<BR>\n" );
document.write( "3. **Last Operation: Conditional ()**<BR>\n" );
document.write( "The arrow (if-then) is the \"main operator\" here. It is applied last, using  as the antecedent and the entire result of the previous step as the consequent.\r<BR>\n" );
document.write( "\n" );
document.write( "### Summary Table\r<BR>\n" );
document.write( "\n" );
document.write( "| Step | Operation | Name | Resulting Sub-expression |<BR>\n" );
document.write( "| --- | --- | --- | --- |<BR>\n" );
document.write( "| 1 |  | Negation |  |<BR>\n" );
document.write( "| 2 |  | Disjunction |  |<BR>\n" );
document.write( "| 3 |  | Conditional |  |\r<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
document.write( "\n" );
document.write( "Would you like me to construct a **truth table** for this expression to see how these operations interact? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );