Let X be the 2-complex obtained from S1 with its usual cell structure by attaching two 2-cells by maps of degrees 2 and 3, respectively.
(a) Compute the homology groups of all the subcomplexes A⊂X and the corresponding quotient complexes X/A.
(b) Show that X≃S2 and that the only subcomplex A⊂X for which the quotient map X→X/A is a homotopy equivalence is the trivial subcomplex, the 0-cell.