Let the operation f of k variables defined on the set {1,2,…,n} be called <spanclass=′latex−italic′>friendly</span> toward the binary relation ρ defined on the same set if f(a1,a2,…,ak)ρ f(b1,b2,…,bk) implies aiρ bi for at least one i,1≤i≤k. Show that if the operation f is friendly toward the relations "equal to" and "less than," then it is friendly toward all binary relations.
B. Csakany combinatorics proposedcombinatorics