Let Σ = {a, b, c}, let L1 be the set of all the strings over Σ which have the same number of a’s, b’s and c’s, and let L2 the set of strings of Σ where all the a’s precede all the b’s and all the b’s precede all the c’s. What is: (a) L1 ∩ L2? (b) L1 ∪ L2? (c) L1? (d) L2? (e) L1 ⊕ L2?

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A:

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Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.