-What’s something new I learned this week?
This week we learned some concepts about
existential claims, contrapositive and converse of statements, but mainly focus
on implication of statements. Through this week’s classes, I
was trained to easily understand a given statement and its implication as well.
-Challenge
In Wednesday’s
class, we were going further on the topic of implication, converse and contrapositive.
I'm still confused about the question on the slide, under the subtitle
Numerical Example:
For the first given
situation, if n is a multiple of 4, why the converse doesn't give us any information?
The first sentence of this question has already defined P(n) is n and Q(n) is
n^2. So, for the converse, we start at the Q(n) first, if n is multiple of 4
(such that 4t for t is a subset of N), then we can know Q(n) must be a multiple
of 4 because Q(n) = n^2 = (4t)^2 = 16t^2, which indicates that Q(n) is true and P(n)
is true as well. However, in the class professor Heap told us to consider the
case of 2, but I think this case is impossible for this situation because if n
= 2, then it is not a multiple of 4, which is contradicting with the given
condition and seems illogical. These are all the reasons why I stuck on this
question for a long time.
-Tutorial
The tutorial exercise for this week is
mainly focus on implication. It is not very challenging for me, but I think we had wasted lots of time on discussing some very silly questions during the tutorial
time. However, the exercise gives me an opportunity to practice the knowledge I
learned from class and I think it is very necessary. I also found that drawing a
Vane Graph is a efficient way to understand the implication of a statement.
