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**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.