Sorry to disagree, Mark...
but the second answer is perfectly correct. One of the entries for "play" (Oxford Dictionary) says:
10 ~ (sth) (on sth)| ~ sth (to sb) ~ sb sth
to perform on a musical instrument; to perform music: [vn] to play the piano / violin / flute
THE is right, and I may understand your question. It's a convention that "the" relates to one particular thing, but here it is more likely to relate to all the guitars in the world.
If you say "I want a sandwich," what you are trying to say is that you want ONE sandwich, but you are not saying which one in particular. (Remember: "a" is the SINGULAR indefinite article.) So if you say "I can play a guitar," you are saying that you can play ONE guitar, but you are not saying which one in particular. Of course, that doesn't make sense: You can play any guitar in the world, not just one. To say that you can play any guitar in the world, you use "the
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