CSC165 week3

This week we learned about the conjunction, disjunction, negation and implication. These topics seem easy at first glance. However, when the negation combines with conjunction and disjunction, the whole statement becomes complicated and much more hard to be understood. In order to understand it, you have to analyse the negation of each part of the statement step by step.

Here is one example in class which I found a little bit difficult to understand and I think it is quite useful for us to understand the further questions.

After taking the negation of the original statement, it seems messy because you are negating the whole statement witch several parts. Therefore we need to negate each of them one by one. First the negation of the universal is exist, so 'for all x' becomes 'there exists a x', then negation of 'exists a y' is 'for all y', now it makes sense, 'there exists a x, for all y such that blablabla'. The last part is P(x,y), it simply becomes not P(x,y), so the negation is 'There exists a x, for all y such that not P(x,y)'.

Each complicated statement can be understood step by step, figure out the meaning of each part in it.