JSFiddle - React, Tailwind, and code Playground
HTML
<div class="a b">class a and b</div>
<div class="b a">class b and a</div>
<hr/>
<div class="a">class a (italic)</div>
<div class="b">class b (bold, not-italic)</div>
<div class="c">class c (tiny, not-bold)</div>
<hr/>
<div class="a c">class ac</div>
<div class="b c">class bc</div>
<div class="c b">class cb</div>
<hr/>
<!-- fork from http://jsfiddle.net/PP9yf/ -->
<p>See <a href="http://stackoverflow.com/q/13808846/287948">related question</a>.
<br>CONCLUSION (testing with chrome and Firefox): with class="x y", x or y overrides, <b>depends on the CSS definition order</b>.
</p>
CSS
.a.b {color: RED;}
.a {font-style: italic;}
.b {font-weight: BOLD; font-style:NORMAL; font-size:130%;}
.c {font-weight: NORMAL; font-size:75%;}