The fact that B is a necessary condition for A to be true, does not exclude the possibility that another proposition, say C, to be also a necessary condition for A to B true.
In other words, it is not difficult to admit that (A-->B) does not imply that (A-->C) is false.
However, saying that B is not only a necessary condition for A to B true, but also a sufficient condition seems to suggest that any other necessary condition is excluded.
Nevertheless, contrary to what intuition tells me, a truth table test shows that : (A iff B) --> ~ (A iff C) is not valid. Which shows that the fact A has B as necessary and sufficient condition does not logically exclude A to have other necessary and sufficient conditions.
The following dialogue illustrates that this is at leat counterintuitive.
A- I'll give you the keys of this flat iff you officially accept to pay 600 dollars a month.
B - OK, I accept, the lease is signed. Let me have the keys.
A - Wait a minute, there is another necessary condition.
B - But you just told me that if I didn't accept to pay, I would not get the keys, but that, as soon as I would accept, I would get them?
A - That's actually what I said. But now I add that you will get the keys iff you accept to pay an advance of 3 monts rent.
B - How long is this conjunction of biconditionals?
How to explain this apparent disagreement between the truth functional analysis and the intuitive understanding of " necessary and sufficient condition"?