Interpreting "p implies q" My Linear Algebra professor had my class work on some proofs, then introduced "truth tables," along with some notation and symbols. I've taken a class on proofs before, but for some reason it didn't provide any background in pure logic, so I'm a bit lost with one thing my LinAlg prof wrote on the board. He listed a few ways to interpret [itex]p \Rightarrow q[/itex]: p implies q, if p then q, q is necessary for p, p is sufficient for q, p only if q I understand the first four items, but the last one doesn't make sense to me. Can someone please explain how it works? Thanks in advance.