(Solved): PLEASE DO NOT USE PREVIOUS ANSWERS!New answer 1. Well formed formulas For each of the following stri ...

1. Well formed formulas For each of the following strings, determine and prove whether it is in WFF, that is, whether it is a well-formed formula. If you think it is in WFF, prove it by providing a construction sequence (and justify each step in the construction sequence). Otherwise, refer to a property that all well formed formulas have, but this one doesn't have (this could be a property shown in class, or one that you identify and prove yourself here by Induction). (a) \( \left.\left(\left(p_{1} \vee\left(\neg p_{1}\right)\right) \rightarrow\left(p_{2} \vee\left(\neg p_{2}\right)\right)\right)\right) \) (b) \( \left(\neg\left(\left(p_{3} \wedge\left(\neg p_{1}\right)\right) \vee\left(p_{1} \wedge p_{2}\right)\right)\right) \) (c) \( \left(p_{1} \vee\left(\neg p_{2}\right)\right) \rightarrow\left(\left(\neg p_{1}\right) \rightarrow\left(\neg p_{3}\right)\right) \) (d) \( \left(p_{2} \rightarrow\left(\left(\left(\neg p_{2}\right) \rightarrow p_{1}\right) \rightarrow\left(\neg p_{1}\right)\right)\right) \)