(a) That's wrong. Although it is true that B breached the contract, it must be remembered that damages are only awarded to compensate for losses arising from the breach. If action taken to mitigate that loss is effective, and the non-defaulting party ends up avoiding all loss or even obtaining a benefit, then damages cannot be claimed.
A specific application of this principle is where goods are purchased but not delivered. If the same goods can be purchased from another supplier either at the same price or more cheaply, then the buyer suffers no loss and cannot claim damages. But if, at the time of the breach, the market price is higher than the original contract price, then the buyer suffers a loss and can claim damages for the difference in price. Indeed, in contracts for the sale of goods, damages are calculated by reference to the market price at the time of the breach regardless of whether or not the buyer actually purchases from another supplier.