If $$P$$, $$Q$$, $$R$$ are Boolean variables, then $$(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})$$ simplifies to

Let fsa and $$pda$$ be two predicates such that fsa$$(x)$$ means $$x$$ is a finite state automation, and pda$$(y)$$ means that $$y$$ is a pushdown automation. Let $$equivalent$$ be another predicate such that $$equivalent$$$$(a,b)$$ means $$a$$ and $$b$$ are equivalent. Which of the following first order logic statements represents the following:

Each finite state automation has an equivalent pushdown automation.

Which one of these first-order logic formulae is valid?

Which one of the first order predicate calculus statements given below correctly expresses the following English statement?

Tigers and lion attack if they are hungry of threatened.