Q:

How can I select an element with multiple classes in jQuery?

I want to select all the elements that have the two classes a and b.
<element class="a b">

So, only the elements that have both classes.
When I use $(".a, .b") it gives me the union, but I want the intersection.

A:

If you want to match only elements with both classes (an intersection, like a logical AND), just write the selectors together without spaces in between:
$('.a.b')

The order is not relevant, so you can also swap the classes:
$('.b.a')

So to match a div element that has an ID of a with classes b and c, you would write:
$('div#a.b.c')

(In practice, you most likely don't need to get that specific, and an ID or class selector by itself is usually enough: $('#a').)

A:

You can do this using the filter() function:
$(".a").filter(".b")

A:

For the case
<element class="a">
  <element class="b c">
  </element>
</element>

You would need to put a space in between .a and .b.c
$('.a .b.c')

