Let X = {0, 1, 2, 3, ..., 14, 15}. For a X, define BINa to be the four-bit binary representation of a. Define R1, a binary relation on X, as follows: For a, b X, aR1b if and only if BINa is a permutation of the bits of BINb. Show that R1 is an equivalence relation, and list its equivalence classes. Define R2, a binary relation on X, as follows: For a, b X, aR2b if and only if BINa differs from BINb in an even number of bit locations. Show that R2 is an equivalence relation, and list its equivalence classes.