CSC165 Week 4

After 4 weeks learning about the logic I found that English is could be so ambiguous. Especially when several antecedents come together with condition, conjunction, disjunction, etc. Even some simple statement can be ambiguous. For example, A and B both guarantees that C is true. I will say if A true and B true then C is true. But some people may think A guarantees C is true individually and B guarantees C is true individually, too.

For week four, we learned about Bi-implication, Transitivity, Mixed Quantifiers and the Proofs.

The Bi-implication means the antecedent is sufficient and necessary for the consequent and vice versa. Say, if P => Q then Q => P and P <=> Q.

When two quantifiers show in one statement, then the order of them will affect the meaning of that statement. The order is a critical problem when we are expressing some mathematical theorems. Sometimes ' for all y, exists an x' is totally different from 'exists an x, for all y'. Therefore we have to pay attention to that when we use mixed quantifiers.

The proofs can give us a better understand about the logic, how thing go at each step. One interesting thing is when we try to proof some thing, we can start it from the conclusion to the assumption first, then write the answer start from assumption. Because sometime, the specific variation of assumption is hard to see.