Which of the following expressions are propositional formulas as defined in the lecture?

$a \lor b$

$\bot$

$x_1 + x_2 \wedge x_3$

$\neg x \lor q \wedge w \rightarrow (a \lor \neq b)$

Which of the following statements are correct?

A propositional formula can be both satisfiable and falsifiable.

A propositional formula can be both satisfiable and unsatisfiable.

A propositional formula can be both valid and falsifiable.

Truth tables are an efficient way to find a model for a propositional formula.

Assume the following propositional formula:
$\phi = (a \lor b \lor c) \wedge (b \lor \neg c) \wedge (\neg a \lor \neg b) \wedge (a \lor c)$.

Which of the following formulas is equivalent to $\phi$?

$a \lor (b \wedge c)$

$(b \lor \neg c) \wedge (\neg a \lor \neg b) \wedge (a \lor c)$

$(a \lor b) \wedge (a \lor c)$

$\neg a \rightarrow (b \wedge c)$