Week 2

     This week in class we learned more about quantifiers.
     First, we reviewed the methods to prove and disprove universal and existential quantification. We did a few examples with data tables and Venn diagrams. Personally, I enjoyed the examples with the Venn diagrams because they helped me visualize the universe where the quantifications take place, which parts of this universe are empty, and which ones contain elements. (Professor Zhang included X and O symbols to show which parts of the Venn diagram are empty and which contains elements) We then used logic symbols to solve more problems with Venn diagrams.
Later, we moved on to quantifiers about sets. We used symbols about sets, which I found useful as a review of these aforementioned symbols I learned about in the past.
We then moved on to evaluating quantified claims. I enjoyed examples Professor Zhang included with Python notation (we were shown two boxes with code and we were to choose which one corresponded with the quantification) since they demonstrated how to convert human language into computer language.
     Next, I got to learn a new concept, sentences and statements. Professor Zhang demonstrated the fundamental differences between sentences and statements, where sentences have subjects and predicates, and a statement is a sentence.
     Then, we talked about predicates. I learned that the predicate can be represented by L(x) (where x has property L.)
     The next topic we covered was implications. I found the relationship between the antecedent and the consequent interesting since it is not causal in nature. One does not cause the other. We learned about contrapositives, or the contradiction of the subject and the predicate, and how to express them in logic symbols. We used if-then statements to decide which part of the sentence was the subject and which was the predicate. I found this part of the lecture challenging as well, but I plan to review the course notes and Professor Zhang's slides to better understand this topic.
      Next, we talked briefly about what I believed to be the most interesting part of the lecture, vacuous truths, a truth that claims that all members of a group have a particular property. Statements such as "pink elephants have 7 legs" could be true because there are no pink elephants around. I found this interesting because it is a type of truth that could apply to members of a group that don't exist (i.e. pink elephants). Next we talked about equivalence (statements that mean the same thing), its vocabulary (i.e. necessary and sufficient.), and idioms (other ways of saying things in math).
     During the tutorials, we solved tutorial exercise number 1. This exercise included some proofs we were to express in natural language for the first questions, and in Venn diagrams in the second question. I found these proof exercise challenging at first, but with some help from T.A. Elias, I was able to solve them. I then took the quiz which was verifying another proof with Venn diagrams and natural language. I think I did fairly well.