Week#7

I found it's easier to perform a proof with the implication format than conjunction or dis-junction formats.

During my tutorial this week on Tuesday, our TA told me the same thing and showed us how to prove the problems with a conjunction as the consequence.

For example,

this is not easy to prove under the original format. So, first we remove the negation.

Then change the conjunction part to the implication format.

De Morgan's Law is the most famous one to use for this situation. And by bi-implication, P(x) => Q(x) is equivalent to NOT P(x) V Q(x). Therefore NOT NOT (y > x) is simply (y > x), and NOT (Ay > Ax) can be re-written as (Ay <= Ax).

Voila!! Now we can pick x, assume y is a typical natural number and assume y > x, then find out if the sequence provided has an example of the existential; the sequence provided is A = 2,3,4,8,9,7,5,3,1,0,0,0,0,0,..... where Ai = 0 for i >= 10.

I have to remember this or I may screw up on the next mid-term again...