Mingyu Liu @ CSC165H1 SLOG3
This is the third time of writing SLOGs for CSC165, in this week's lecture, we have finished talking about the language of MATH which is called 'Bi-implication'. Initially, professor posts some slides in order to review the former lecture which is a means to place a foundation for further lecture as well as recall my memories. For example, P => Q is equivalent to -/P v Q and -/(P => Q) is equivalent to P ^ -/Q. I believe this part provides me a great tip which I can be used for exercises in the lecture after. Then our professor talks about bi-implication which can be utilized to translate from conjunction of two disjunctions and also from disjunction to conjunction. The method of doing that requires mathematical ways which are distributive way. After bi-implication, the lecture also covers the negation of bi-implication which is a little difficult than bi-implication because it requires 'De Morgan's law'; therefore, I believe this part is what I grasp well in this week's lecture.
Moreover, transitivity and proof which I believe to be not that difficult. For example, the transitivity of this expression (P(x) => Q(x) ^ (Q(x) => R(x)) is P(x) => R(x). the reason why it is not difficult, because professor uses a visual way to teach us the definition of transitivity which means that if P implies Q and Q implies R, then Q must include P and R must include Q; therefore, R includes P for sure. For the proof part, professor teaches us about how to find the chain with ^ and v. For example, if there are no particular features in the expression, you will just have to start from downward to upward; otherwise, you can start from upward.
The interesting part of this week's lecture is that the professor makes a small activity of lecture which requires a group of three people and thinks the problem together. This is absolutely interesting because it improves the interaction between the lecture and students.
In conclusion, we have finished the language of math in this week's lecture and the difficult part which I encounter is mixed quantifiers. According to the professor, the language of math is not only for using symbols but understanding and expressing in a logical way. Finally, I hope my first test will be good.
Third slog
Mingyu Liu
Moreover, transitivity and proof which I believe to be not that difficult. For example, the transitivity of this expression (P(x) => Q(x) ^ (Q(x) => R(x)) is P(x) => R(x). the reason why it is not difficult, because professor uses a visual way to teach us the definition of transitivity which means that if P implies Q and Q implies R, then Q must include P and R must include Q; therefore, R includes P for sure. For the proof part, professor teaches us about how to find the chain with ^ and v. For example, if there are no particular features in the expression, you will just have to start from downward to upward; otherwise, you can start from upward.
The interesting part of this week's lecture is that the professor makes a small activity of lecture which requires a group of three people and thinks the problem together. This is absolutely interesting because it improves the interaction between the lecture and students.
In conclusion, we have finished the language of math in this week's lecture and the difficult part which I encounter is mixed quantifiers. According to the professor, the language of math is not only for using symbols but understanding and expressing in a logical way. Finally, I hope my first test will be good.
Third slog
Mingyu Liu
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