A bit string is a sequence of zeros and ones. For example 0101 and 1001 are two bit strings of length four that agree in their third and fourth bit. Show that the relation R consisting of all pairs ( x , y ) of binary strings that agree in their first and third bits is an equivalence relation on the set of all bit strings of length three or more. Write the equivalence classes of this relation and show that they form a partition of the set of all bit strings of length three or more.

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