Should menu titles (h1, h2, h3...) be inside or outside the <nav> tag?

Question

Let's say I want to write a simple menu in HTML5.

Should I write like this:

<h1>My Menu</h1>
<h2>Submenu 1</h2>
<nav>
    <ul>
        <li><a href="#">Link 1</a></li>
        <li><a href="#">Link 2</a></li>
        ...
    </ul>
</nav>
<h2>Submenu 2</h2>
<nav>
    <ul>
        <li><a href="#">Link 1</a></li>
        <li><a href="#">Link 2</a></li>
        ...
    </ul>
</nav>

Or like this:

<nav>
    <h1>My Menu</h1>
    <h2>Submenu 1</h2>
    <ul>
        <li><a href="#">Link 1</a></li>
        <li><a href="#">Link 2</a></li>
        ...
    </ul>
    <h2>Submenu 2</h2>
    <ul>
        <li><a href="#">Link 1</a></li>
        <li><a href="#">Link 2</a></li>
        ...
    </ul>
</nav>

In other words, should the titles be inside or outside the <nav> tag?

Thanks.

Answer 1

According to the HTML5 spec, "nav" is a "section" and a section "is content that defines the scope of headings and footers." The W3C example for the nav section shows h tags in the the nav.

http://www.w3.org/TR/html5/sections.html#the-nav-element

Answer 2

h tags are for the structure of the content of the page. I wouldn't say navigation is part of the content of the page, so it doesn't make sense to me to have h tags in the navigation.