(b) That's wrong. This case involves a unilateral mistake on A's part. But it is important to notice that, in this example, B is aware that A has made a mistake. In such circumstances, even though there is sufficient objective agreement for a binding contract, a court will most likely provide equitable relief.
The basis of this relief is that it is unconscionable for a party to enforce a contract when they know the other party has contracted on disadvantageous terms under a misapprehension of fact, and when, knowing this, they act in a way that prevents discovery of the true facts. In the example, B has not questioned what he knows is a likely mistake in the written offer. The court will therefore either refuse to enforce the contract, or set it aside as void, and order both parties to restore whatever they have received under the contract.