What was challenging for me this week?

1)    I was having problems how to translate an english statement to symbolic language? Especially, the first question from this week’s tutorial assignment was pretty challenging for me. I felt like we did not learn how to solve this kind of problems in the lecture since this week we learned about only different laws, scoping, negation and conjunction. I felt very frustrated. I really wished we did some example questions similar to the one in the tutorial assignment during the class! 

      First I tried to use [intersection, empty set, union] and wrote a statement. However, when I checked the Larry Zhang’s slides [I go to Danny’s session, not Zhang’s but wanted to see what he was doing, I thought it might help my understanding and actually which did! yay! :)] 
I noticed that conjunctions V and ^  are used for predicates and ∩ , ∪ are used for sets. This small detail helped me a lot to clarify my understanding of the topic and see why I cannot find the solution. 

2)    2b on the tutorial assignment was challenging for me.

Steps I took: 

     i) I went over the lecture notes again and read the course reading [in which I came to learn that question 2a and 2d are True since they are part of the quantifier distributor law]. However, they didn’t help me much with the b.

     ii) Drew Venn diagram to find the solution. 

Venn diagram helped me to find the solution!

             2b:      ∃x ∊ D, P(x) ∧ Q(x) <=> (∃x ∊ D, P(x)) ∧ (∃x ∊ D, Q(x)) 

                                                              So it’s False!

Problem: as an international student, who are taught math in German, sometimes understanding the English math terms could be challenging, especially when prof is speaking very fast in the class and you cannot write down the word since you don’t know how to spell them. 

Solution: However, last week and this week every day after my class, i went over my lecture slides and make sure I understood every single word on it. Plus the course reading was a great help to me. I found the math terminology [exp: universe, intersection etc] on the course reading and now the course material is more clear to me.

Problem: implications! in the class Danny gave this following example: “if you eat your vegetables, you will get desert” and added that the only and only way this implication is wrong is the time when I eat my vegetables but do not get dessert. Although this makes sense, I was pretty confused why this following statement is not false: I get my desert although i didn’t eat my vegetables. if P is wrong and Q is true then this statement is correct, said Danny. However, i still cannot understand why until I read my course reading. Now I realized that an implication is a one way statement. P => Q. if I eat my vegetables, I get desert. This is the only condition I should focus on the implication. This implication is only correct from left to right, doesn’t work from right to left [one way only]. Saying I got desert although i didn’t have vegetables is not a counter argument for our implication.  this is a different scenario/ statement,  it’s not what we are talking about!

what material challenged me this week?

- translating the problem from a sentence to a venn diagram. I learned about venn diagram when I was at middle school. So first, I had to refresh my memory. Secondly, I needed to practice more. When I read a sentence I can write it done by using symbols. However, it is still challenging for me to draw a diagram and indicate which part of it is empty and which part is full with elements from that set.