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To put a set in correspondence with another means to pair off elements of the first set with those of the other one.
For example we can put the set {a, b, c} in correspondence with {1, 2, 3} by pairing a with 1, b with 2 and c with 3.
There is not a similar correspondence of {a, b} with {1, 2, 3}, although we can form a correspondence of {a, b} with a subset of {1, 2, 3}, for example, with {2, 3}.