Explanation Given information: The given subset relation on the power set P = { a , b , c , d } . Calculation: The following is the algorithm given using which the topological sorting is to be found out for the given relation- The relation ≺ is partial order on the sets. So now using the algorithm on the set A Pick any minimal element x in A . Set A ' = A − { x } . Repeat the following steps a − c while A ' = ϕ a ) Pick any element in A ' . b ) Define x ≺ y . c ) set A ' : = A − { y } So now let us follow the above algorithm for the given power set A { ϕ , { a } , { b } , { c } , { d } , { a , b } , { a , c } , { b , c } , { a , d } , { b , d } , { b , c } , { c , d } , { a , b , d } , { a , c , d } , { b , c , d } , { a , b , c , d } } The set has the minimal element ϕ , so removing it, The set will be A ' = A − ϕ . Now the remaining minimal elements will be a , b , c . So till now the topological sorting order will be ϕ ≺ { a } , ϕ ≺ { b } , ϕ ≺ { c } . Also, for the second set of minimal elements as { a } ≺ { b } ≺ { c } . Further pick the next level of elements { a } ≺ { a , b } , { a } ≺ { a , c } , { b } ≺ { a , b } , { b } ≺ { a , c } , { c } ≺ { a , b } , { c } ≺ { a , c } . So till now the topological order sorting is ϕ ≺ { a } ≺ { b } ≺ { c } ≺ { a , b } ≺ { a , c } ≺ { b , c } . Now continuing in the same way, the next level of ordering { a , b } ≺ { a , b , c } , { b , c } ≺ { a , b , c } , { a , c } ≺ { a , b , c }

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Author: EPP, Susanna S.

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Chapter 8.5, Problem 48ES

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To find the topological sorting for the subset “subset” relation on the given set.

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Chapter 8.5, Problem 47ES

Chapter 8.5, Problem 49ES

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To find the topological sorting for the subset “subset” relation on the given set.

Solution Summary: The author explains the algorithm used to find the topological sorting for the subset relation on the given set.

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To find the topological sorting for the subset “subset” relation on the given set.

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Chapter 8 Solutions