---------------------------------------------------------
$this && $that   |    If $this is true, and $that is true
                 |    return the value of the last
                 |    expression evaluated ($that).
-----------------+---------------------------------------
$this || $that   |    If $this evaluates true, stop 
                 |    evaluating, we're done.  Otherwise
                 |    evaluate $that for truthfulness.
                 |    If $that evaluates true, return 
                 |    the value of $that.
---------------------------------------------------------
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That doesn't explain what is returned if $that is false. May I suggest the following (which is shorter, symmetric, and explains the return value on failure).

---------------------------------------------------------
$this && $that   |    If $this is true, return $that,          
                 |    else return $this.
-----------------+---------------------------------------
$this || $that   |    If $this is true, return $this,
                 |    else return $that.
---------------------------------------------------------
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Abigail