Narasimha #24: the way you formulated your propositions, it seems to me that A true gives B true! Unless you meant A=it rains B=the match is happening , in which case A cannot imply B (since true cannot imply false). You considered the negative statement instead!
To sum up: A=it rains, B=match is on, then A does not imply B and B does not imply A. However \\(A\Rightarrow\neg B\\).