Consider the following 7 clauses . GAV B) . (AVC) . BVC) . (BVA) . CVA) (a) Fill

Question

Consider the following 7 clauses . GAV B) . (AVC) . BVC) . (BVA) . CVA) (a) Fill out the truth table and see if you have an assignment of variables that satisfies ALL 7 clauses. (b) The GSAT algorithm for finding a model to satisfy a set of clauses uses hill-climbing search. It starts by choosing a random assignment of truth values to all the variables. At each iteration, one variable assignment is made which increases the number of sat- isfied clauses, i.e., the number of clauses which are true. The algorithm stops when no assignment increases the number of satisfied clauses. Use GSAT to find a global maxi- mum, i.e., an assignment that satisfies all clauses. Use the following initial assignment: As T(rue), B = False), and C = F.

Explanation / Answer

The truth table is given below.

Please note that the symbol ~ before a variable means NEGATION. And the symbol v means OR
e.g. ~A v B = A' + B
According to OR rule if any of the variables in the expression is True then resultant is True and a negation inverts the value from True to False and from False to True.

A B C ~A ~B ~C ~A v B ~A v C ~B v C ~B v A ~C v A ~C v B ~A v ~B v ~C T T T F F F T T T T T T F T T F F F T T F F T T T T T F T F T F F T T T T F T T F F F T T F F T T T T T F T T T F F T T T F F T T F T F T F T T T F F T T T F F T T T F T T T T F F T F F F T T T T T T T T T T

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