(a) No. Offers don't stay open forever. They expire after a reasonable time, or after any period set by the person making it. And an offer can be withdrawn by the person making it at any time before it is accepted. In this case A clearly withdraws the offer before B accepts it.

To prevent this from happening, a person who wants time to consider an offer would need to obtain an option. An option is itself a binding contract which obliges the person making an offer to keep it open for a specified period.