document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164610>Question 1164610</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\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854340 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2264)</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=854340\">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 $p \to q \lor \neg r$, we follow the standard **Order of Logical Precedence**. Much like \"PEMDAS\" in algebra, logic has a hierarchy that dictates which operator is evaluated first.\r<BR>\n" );
document.write( "\n" );
document.write( "The standard order is:<BR>\n" );
document.write( "1.  **Negation** ($\neg$ or $\sim$)<BR>\n" );
document.write( "2.  **Conjunction** ($\land$)<BR>\n" );
document.write( "3.  **Disjunction** ($\lor$)<BR>\n" );
document.write( "4.  **Conditional** ($\to$)<BR>\n" );
document.write( "5.  **Biconditional** ($\leftrightarrow$)\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 the rules above, here is the step-by-step order for your expression:\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **First: Negation ($\sim r$)**<BR>\n" );
document.write( "    The \"NOT\" operator has the highest priority. You must determine the truth value of $\sim r$ before it can be used in any other operation.<BR>\n" );
document.write( "2.  **Second: Disjunction ($q \lor \sim r$)**<BR>\n" );
document.write( "    The \"OR\" operator is next in the hierarchy. You take the result from the first step and evaluate it against $q$.<BR>\n" );
document.write( "3.  **Last: Conditional ($p \to \dots$)**<BR>\n" );
document.write( "    The \"IF...THEN\" operator has the lowest priority in this expression. It acts as the \"main connective,\" linking $p$ to the result of the entire right-hand side.\r<BR>\n" );
document.write( "\n" );
document.write( "### **Summary Table**<BR>\n" );
document.write( "| Order | Operation | Symbol |<BR>\n" );
document.write( "| :--- | :--- | :--- |<BR>\n" );
document.write( "| 1st | Negation | $\sim$ |<BR>\n" );
document.write( "| 2nd | Disjunction | $\lor$ |<BR>\n" );
document.write( "| 3rd | Conditional | $\to$ |\r<BR>\n" );
document.write( "\n" );
document.write( "**Visual Grouping:** If you were to add parentheses to show this order, the expression would look like this: $(p \to (q \lor (\sim r)))$.\r<BR>\n" );
document.write( "\n" );
document.write( "Are you building a truth table for this expression, or just practicing the syntax? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );