Solution
= Solution
Taking transitive closure adds only descendants of existing members, whose ranks are lower. Thus the supremum of member ranks, and hence the rank of the set, is unchanged: $\rho(x)=\rho(\operatorname{tcl}x)$.
= Solution
Taking transitive closure adds only descendants of existing members, whose ranks are lower. Thus the supremum of member ranks, and hence the rank of the set, is unchanged: $\rho(x)=\rho(\operatorname{tcl}x)$.