A definition of wedge sum can be found here:

http://en.wikipedia.org/wiki/Wedge_sum

My professor has claimed that wedge sums of path connected spaces are well-defined up to homotopy equivalence, independently of choice of base points x0 and y0.

Recall homotopy equivalence of X and Y means that there is f:X->Y and g:Y->X continuous with gf and fg homotopic to the identity.

With these definitions, please prove my professor's claim, which I have failed to do for a week. (It is left as an exercise in his lecture.)

Thanks.