What is the proper way to check and uncheck a checkbox in HTML5?

For checked state

Older browsers may need:

<input type="checkbox" checked="checked" />

But nowadays simply do:

<input type="checkbox" checked />

For unchecked state

Remove checked attribute, like:

<input type="checkbox" />

Reference: http://www.w3.org/TR/html-markup/input.checkbox.html#input.checkbox.attrs.checked