IGNOU MTE 13 2018 - Write (x z) (yz') in CNF and DNF.

Question

Write (x $\wedge$ z) $\vee$ (y $\vee$ z') in CNF and DNF.

14 Feb 2018

Answer :

Word Count : 547

This is an assignment problem, which can be solved using the Hungarian algorithm to minimize the total time taken. ### Step 1: Construct the Cost Matrix The given table represents the time taken by each employee (A to E) for each job (I to V): | Employee | Job I | Job II | Job III | Job IV | Job V | |----------|-------|--------|---------|--------|-------| | A | 10 | 5 | 13 | 15 | 16 | | B | 3 | 9 | 18 | 13 | 6 | | C | 10 | 7 | 2 | 2 | 2 | | D | 7 | 11 | 9 | 7 | 12 | | E | 7 | 9 | 10 | 4 | 12 | We will apply the Hungarian Algorithm to find the optimal assignment. --- ### Step 2: Reduce the Matrix #### Row Reduction Subtract the smallest value in each row from all elements in that row: | Employee | Job I | Job II | Job III | Job IV | Job V | Min Value Subtracted | |----------|-------|--------|---------|--------|-------|----------------------| | A | 5 | 0 | 8 | 10 | 11 | 5 | | B | 0 | 6 | 15 | 10 | 3 | 3 | | C |

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