Find a system of distinct representatives for the following sets: {b,e,i,l}, {a,j,m}, {c,f,k}, {b,h,i,l}, {d,g,m}, {e,h,k,l}, {a,d,j}, {g,j,m}, {c,e,k}, {a,g,j}, {f,h,i}, {d,j,k,m}, {b,c,f}.
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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 =13
Total no. of sub sets =13
Hence,
System of distinct representatives,