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<b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">(3) <font color="#FF0000">The Satisfiability Problem</font>
<i><font color="#0033CC">formulas</font> </i>~ variables x1, x2, ...., xn (true, false)
operator <img src="IMAGE/and.gif" width="18" height="18"> (and) <img src="IMAGE/or.gif" width="18" height="17"> (or) <img src="IMAGE/not.gif" width="26" height="13"> (not)
<font color="#FF0000">rules:</font>
1. A variable is an expression
2. If x and y expressions, then <img src="IMAGE/not.gif" width="20" height="9">x, x <img src="IMAGE/and.gif" width="12" height="13"> y, x <img src="IMAGE/or.gif" width="12" height="13"> y, are expression
3. Parentheses can be used to alter the normal order of
evaluation, which is <img src="IMAGE/not.gif" width="20" height="9"> before <img src="IMAGE/and.gif" width="12" height="13"> before <img src="IMAGE/or.gif" width="12" height="13"> .
<font color="#FF0000">example:</font>
the expression: x1 <img src="IMAGE/or.gif" width="12" height="13"> ( x2 <img src="IMAGE/and.gif" width="12" height="13"> <img src="IMAGE/not.gif" width="20" height="9"> x3 ) is a <i><font color="#0033CC">formula.</font></i>
<i> If </i>x1 = x3 = false, x2 = true,
<i>Then</i> the value of the expression
= false <img src="IMAGE/or.gif" width="12" height="13"> ( true <img src="IMAGE/and.gif" width="12" height="13"> <img src="IMAGE/not.gif" width="20" height="9"> false) = false <img src="IMAGE/or.gif" width="12" height="13"> true = true
<i>The<font color="#FF0000"> satisfiability problem</font><font face="Arial, Helvetica, sans-serif" size="4"> for formulas of the propositional calculus
ask if there is an assignment of values to the variables that
causes the value of the expression to be True</font></i>
</font></b></pre>
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