The Web Hypertext Technology Working Group (WHATWG) specifies that both the and tags are to be used as a last resort when no other element is more appropriate.
MaximumPC
The truth is: it’s all semantics. The tag does not specifically imply a strong emphasis on a particular word, nor does the tag indicate that there is light emphasis. You could argue that you want the elements to convey either meaning.
The bold and italic font elements do not have to be considered illegal. Rather, it’s that they’re hardly used in the proper context. The and tags should never be used solely for the purpose of stylizing text and especially not for headers. After all, that’s what CSS is for.
The Modern Alternative: Use the and tag to bold and italicize, respectively.