how do I select a div with class "A" but NOT with class "B"?

I have some divs:

<div class="A">"Target"</div>
<div class="A B">"NotMyTarget"</div>
<div class="A C">"NotMyTarget"</div>
<div class="A D">"NotMyTarget"</div>
<div class="A E">"NotMyTarget"</div>

Is there a CSS selector that will get me the div containing Target but not the divs containing NotMyTarget?

Solution must work on IE7, IE8, Safari, Chrome, and Firefox

Edit: So far Nick is the closest. It's clumsy and I don't like the solution, but at least it works:

.A
{
   /* style that all divs will take */
}
div.B 
{
  /* style that will override style .A */
}

You can use the attribute selector to match the div that has only one class:

div[class=A] {
  background: 1px solid #0f0;
}

If you want to select another div that has multiple classes, use quotes:

div[class="A C"] {
  background: 1px solid #00f;
}

Some browsers do not support the attribute selector syntax. As usual, "some browsers" is a euphemism for IE 6 and older.

See also: http://www.quirksmode.org/css/selector_attribute.html

Full example:

<!DOCTYPE html>
<html>
<head>
  <style>
    .A { font-size:22px; }
    .B { font-weight: bold; border: 1px solid blue; }
    .C { color: green; }

    div[class="A"] {
      border: 1px solid red;
    }
    div[class="A B"] {
      border: 3px solid green;
    }
  </style>
</head>
<body>
  <div class="A">"Target"</div> 
  <div class="A B">"NotMyTarget"</div> 
  <div class="A C">"NotMyTarget"</div> 
  <div class="A D">"NotMyTarget"</div> 
  <div class="A E">"NotMyTarget"</div> 
</body>
</html>

EDIT 2014-02-21: Four years later, :not is now widely available, though verbose in this specific case:

.A:not(.B):not(.C):not(.D):not(.E) {
  border: 1px solid red;
}

Unfortunately, this doesn't work in IE 7–8 as specified in the question: http://caniuse.com/#search=:not

.A:not(.B) {}

But guess who doesn't support that... Indeed, IE<=8.

how do I select a div with class "A" but NOT with class "B"?

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