In 59.a), the titration is between a weak acid and a strong base. At the equivalence point, you're gonna end up with water, sodium and the conjugate base of the weak acid. That base in aqueous solution establishes an equilibrium. So, to determine the pH at the equivalence point, you have to take into consideration the amount of conjugate base that forms and then the equilibrium that is establishes. Same for the halfway point, only in this case you have a mixture of conjugate base and weak acid.
These exercises are much simpler if you write the neutralization reactions btw.