Identify 4 distinct infinite s

Identify 4 distinct infinite sets of real numbers A B C and D so that each set is contained in the next one and so that A matches B, B matches C, but C does NOT match D. (There are many possible correct answers. Also it would be easiest to use standard sets of numbers such as NAT or RAT etc. as choices for A ,B,C, and D). Justify each conclusion
