**What I think I know**

* *A priori* knowledge that can be gained by contemplating only the meaning of a statement's words.
* *A posteriori* knowledge can be gained only by comparing a statement's meaning with the state of affairs.
* *Analytic* knowledge that can be gained by contemplating only the meaning of a statement's words.
* **Synthetic** knowledge that is not gained analytically

**The problem**

I understood the definitions of 'a priori' and 'analytic' to be extensionally identical. The definitions of 'synthetic' and 'a posteriori' that I used here may be different, but I'm doubtful - as it seems to me that there are only two ways of verifying a statement: deduction, and induction. From what I (probably, incorrectly) understand, 'A priori' and 'analytic' refer to 'deduction'; this leaves 'synthetic' and 'a posteriori' to share 'induction'. Yet, people who know more about philosophy than I know about it, and who have thought about these terms more than I have thought about them, seem to be able to distinguish between the two sets of terms. 

**The question**

What distinguishes 'A priori' from 'analytic'?

What distinguishes 'synthetic' from 'a posterior'?

Thank you