More on negation-- Week 3

As i mention in Week 1's blog, negation means negative of the original 

statement. In this week, we put all the universal  , existing quantifier 

and implication together and we try to negation them all  at once. Here 

is one example:

¬(∀ X∈R, ∃ y∈R, P⇒Q)⇔  (∃ x∈R, ∀ y∈R, ¬(¬PvQ) )
(∃ x∈R, ∀ y∈R, P^ ¬Q)

although, negation of such long statement seems to be hard at the beginning, 

but after many times practicing the negation, it becomes pretty computational 

and easy.