about necessary and sufficient condition, again Here I have a sentence picked up from a first year book:

The statement “if A then B” is equivalent to the statement “A is a sufficient condition for B” and to the statement “B is a necessary condition for A"

I understand the first part, but I cannot see how the statement “if A then B”
leads to the conclusion that “B is a necessary condition for A".
Is a sufficient condition always a necessary condition?
Hope anyone could help for some explanation and examples.
Thanks

"A is sufficient for B" is $A\to B$.  Also stated as "If A then B". 
This means that the truth of A garantees the truth of B, although B might be true when A is not.
That is either A is false or B is true.

"B is necessary for A" is $B\leftarrow A$.
This means that A cannot be true when B is not, but that A may not be true when B is.
That is either A is false or B is true.

Ergo they are equivalent.  $$A\to B \quad\iff\quad B\leftarrow A$$
