Showing logical equivalence of these two formulas I have the following statement in propositional logic: (¬g v s1 v ¬s2) ^ (¬g v ¬s1 v s2) ^ (¬g v s1 v s2) (1) I want to show equivalence to this statement: (¬g v s1) ^ (¬g v s2) (2) I can use the distributive property on (1) to obtain the following statement: (¬g v s1 v ¬s2) ^ (¬g v ¬s1 v s2) ^ ((¬g v s1) v (¬g v s2)) (3) I can see that the last conjunct renders the first two 'redundant', but I do not know that steps to take to show logical equivalence to (2). Can anyone help? Thank you

The formula :

> (2) $(¬g \lor s_1) \land (¬g \lor s_2) $

is equivalent to [recall that : $p \lor F \equiv p$ and $p \land \lnot p \equiv F$]:

> $[(¬g \lor s_1) \lor (s_2 \land ¬s_2)] \land [(¬g \lor s_2) \lor (s_1 \land ¬s_1)]$.

By Distributive property we have :

> $(¬g \lor s_1 \lor s_2) \land (¬g \lor s_1 \lor ¬s_2) \land (¬g \lor s_1 \lor s_2) \land (¬g \lor ¬s_1 \lor s_2)$.

Removing the repeated term we have :

> > (1) $(¬g \lor s_1 \lor s_2) \land (¬g \lor s_1 \lor ¬s_2) \land (¬g \lor ¬s_1 \lor s_2).$