Wondering if I can get some clarification on these, or if any of the diagrams are wrong?

A requires B = A --> B

A is required for/by B = A --> B

A is necessary for B = A --> B

A necessitates B = A --> B

A needs B = A --> B

All that is required for A is B = A --> B

Also, how could one use require/necessary such that it is B --> A, with B appearing in the sentence first?

Thanks a lot!