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1. i. Give an example of a Boolean formula F which contains at least 2 different...

1. i. Give an example of a Boolean formula F which contains at least 2 different variables, and where F is satisfiable and its negation (not)F is not satisfiable.

ii. Give an example of a Boolean formula F which contains at least 3 different variables, and where F is satisfiable and has exactly 5 satisfying truth assignments.

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Answer #1

i)

Satisfiable formula: (A v A') v (B v B')

Unsatisfiable formula: (A ∧ A') ∧ (B ∧ B')

ii)

Satisfiable formula: (A v A') v (B v B') v (C v C')

Unsatisfiable formula: (A ∧ A') ∧ (B ∧ B') ∧ (C ∧ C')

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