Find a system of distinct representatives for the following sets: {a, c, f}, {b, g}, {c, d, h}, {a, d, j}, {e, i, k}, {f, j, l}, {b, i, k}, {e, g}, {a, c, f, h, l}, {g, k}, {b, e, i}, {d, h, j}.
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By Hall's Theorem,
An SDR (System of distinct representatives) is a collection of distinct elements
Let be subsets of A
has an SDR if
In our case
Total no. of distinct elements =12
Total no. of sub sets =12
Hence,
System of distinct representatives,