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I replied in the question. The question is more subtle than I first thought, but it is at the level of a 1st year grad algebraic topology course out of a book like Hatcher's.
I still don't think it's appropriate for MO, though.
I can't imagine offering this as a homework problem in first year algebraic topology without a hint or two. This is in no way obvious unless you know the right sort of tricks, which might or might not get dealt with in a first year course, depending on the level. I think it is a perfectly fine question.