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It's from a Discrete Mathematics course and it requires a step by step proof with logical equivalences and deductions made based on the laws of logic.

A,B,C and D are all on the same canoe team. They don't know what sitting order they should make and all of them have a certain wish. Could they find a sitting arrangement that satisfies all their wishes?

A: I'd like to sit at the back only if I sit next to B.

B: I don't want to sit next to C and I don't want to sit at the back.

C: If I sit at the back, I don't want to sit next to A.

D: I want to sit next to B or not next to A, and if I can't sit at the front, then I want to sit at the back.

I need help with getting started. I can attack the problem verbally(so to speak). I can provide an arrangement which would fulfill every wish. It's C A B D, C being at front and D being at the back. However, in my course this proof wouldn't be good enough, and therefore I need to provide a more rigorous one. Any suggestions? I was thinking of making a statements for every possibility, but proving it that way seems tiresome and redundant... Just tell me in which direction I should head, and I'll give it a go on my own.