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Which binary Functions satisfy Semigroupoid

Calculation to determine which of 16 binary functions satisfy the associative law of SEMIGROUPOID and which ones don't

Info

Source Code ( 115 lines )

<?php

$functions = array( 
    "0"=>"0000",
    "&"=>"0001",
    "x & ~y"=>"0010",
    "x"=>"0011",
    "~x & y"=>"0100",
    "y"=>"0101",
    "xor"=>"0110",
    "or"=>"0111",    
    "nor"=>"1000",
    "~nor"=>"1001",
    "~y"=>"1010",
    "x | ~y"=>"1011",
    "~x"=>"1100",
    "~x | y"=>"1101",
    "nand"=>"1110",
    "1"=>"1111");

foreach ($functions as $key=>$function)
{
    echo "<br><table border=1 cellpadding=3 cellspacing=0>";
    echo "<tr><td colspan=8 align=center bgcolor=silver><font color=blue><b>$key</b></font></b></td></tr>";
    echo "<tr><td align=center>x</td><td align=center>y</td><td align=center>z</td><td align=center>(y+z)</td><td align=center>x+(y+z)</td><td align=center>(x+y)</td><td align=center>(x+y)+z</td><td>x+(y+z)=(x+y)+z</td>";
    foreach($xarr=array(false,true) as $x)
    {    
        foreach($yarr=array(false,true) as $y)
        {
            foreach($zarr=array(false,true) as $z)
            {

                if($x){$displayX = "T";}
                else  {$displayX = "F";}

                if($y){$displayY = "T";}
                else  {$displayY = "F";}

                if($z){$displayZ = "T";}
                else  {$displayZ = "F";}

                echo "<tr>";
                echo "<td> &nbsp $displayX &nbsp </td><td> &nbsp $displayY &nbsp </td><td> &nbsp $displayZ &nbsp </td>";    
                
                $leftside = operation($x,operation ($y,$z,$function),$function);
                $rightside = operation(operation($x,$y,$function),$z,$function);
        
                echo "<td align=center>".operation ($y,$z,$function)."</td>";
                echo "<td align=center>".$leftside."</td>";

                echo "<td align=center>".operation($x,$y,$function)."</td>";
                echo "<td align=center>".$rightside."</td>";    

        
                if($leftside == $rightside)
                {
                    echo "<td align=center>";                
                    echo "<font color=green>";
                }     
                else
                {
                    echo "<td bgcolor=silver align=center>";                
                    echo "<font color=red>";
                }     

                echo "$leftside = $rightside";

                echo "</font></b>";
                
                echo "</td>";
    
                echo "</tr>";
            }
        }
    }
    echo "</table>";
}

    echo "<br><br>";

    echo"<table bgcolor=silver width=80%>";
    echo "<tr><td>";
    $source = 'semigroupoid.php';
    highlight_file($source);
    echo "</td></tr>";
    echo "<table>";


function operation($firstValue,$secondValue,$functionID)
{
    #$functionResults = array ($functionID[0],$functionID[1],$functionID[2],$functionID[3]);

    if( (!$firstValue) && (!$secondValue) )
    {
        return $functionID[0];
    }

    if( (!$firstValue) && ($secondValue) )
    {
        return $functionID[1];
    }

    if( ($firstValue) && (!$secondValue) )
    {
        return $functionID[2];
    }

    if( ($firstValue) && ($secondValue) )
    {
        return $functionID[3];
    }

}

?>