Discuss and explain whether there is valid consideration for each of the following promises:

a$.$ A and $B$ entered into a contract for the purchase and sale of goods. A subsequently promised to pay a higher price for the goods when B refused to deliver at the contract price.

b$.$ A promised in writing to pay a debt, which was due from $B$ to $C,$ on C$\text{'}$s agreement to extend the time of payment for one year.

c$.$ A orally promised to pay $$150$ to her son, B$,$ solely in consideration of past services rendered to A by B$,$ for which there had been no agreement or request to pay.