Question

A conjunctive normal form (CNF) is a boolean expression which is a conjunction of disjunctions. For example, $\alpha = (a \lor b) \land (\bar{a} \lor b \lor c)$ is such a CNF where $\bar{a}$ denotes negation of the boolean variable a. A truth valuation $v$ that makes $v(\alpha)$ True is given by $v(a) = v(b) = v(c) = $True. It turns out, but we forego the proof, that every formula can be written in a conjunctive normal form with three literals (either variables or their negations) in each clause. We call such a formula a 3-CNF formula. (a) Give an explicit truth valuation (that is truth values for each of the variables below) for the following formula that make the formula evaluate to true: $\beta = (a \lor b \lor c) \land (a \lor b \lor \bar{c}) \land (\bar{a} \lor b \lor c) \land (\bar{a} \lor b \lor \bar{c}) \land (\bar{a} \lor \bar{b} \lor c) \land (a \lor \bar{b} \lor c) \land (a \lor \bar{b} \lor \bar{c})$

          A conjunctive normal form (CNF) is a boolean expression which is a conjunction of disjunctions. For example, $\alpha = (a \lor b) \land (\bar{a} \lor b \lor c)$ is such a CNF where $\bar{a}$ denotes negation of the boolean variable a. A truth valuation $v$ that makes $v(\alpha)$ True is given by $v(a) = v(b) = v(c) = $True. It turns out, but we forego the proof, that every formula can be written in a conjunctive normal form with three literals (either variables or their negations) in each clause. We call such a formula a 3-CNF formula.
(a) Give an explicit truth valuation (that is truth values for each of the variables below) for the following formula that make the formula evaluate to true:
$\beta = (a \lor b \lor c) \land (a \lor b \lor \bar{c}) \land (\bar{a} \lor b \lor c) \land (\bar{a} \lor b \lor \bar{c}) \land (\bar{a} \lor \bar{b} \lor c) \land (a \lor \bar{b} \lor c) \land (a \lor \bar{b} \lor \bar{c})$

A conjunctive normal form (CNF) is a boolean expression which is a conjunction of disjunctions. For example, α = (a b) (a̅ b c) is such a CNF where a̅ denotes negation of the boolean variable a. A truth valuation v that makes v(α) True is given by v(a) = v(b) = v(c) =True. It turns out, but we forego the proof, that every formula can be written in a conjunctive normal form with three literals (either variables or their negations) in each clause. We call such a formula a 3-CNF formula.
(a) Give an explicit truth valuation (that is truth values for each of the variables below) for the following formula that make the formula evaluate to true:
β = (a b c) (a b c̅) (a̅ b c) (a̅ b c̅) (a̅b̅ c) (a b̅ c) (a b̅c̅)

Added by David R.

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