During week 4 I actually was able to understand some of the concepts that we learned in class. For instance, we learned about different laws which I was able to pick up easily. I saw many similarities between these laws and what I learned in Advanced Functions, because some of the laws require expansion. Although were not supposed to memorize these laws, there were two that I was able to understand, and apply easily to my 165 work.
De Morgan's Law
¬ ( A ∧ B ) ⇔ ( ¬A ∨ ¬B )
Not A and B is true if and only if not A or not B true
Not A and B is false if and only if not A or not B is false
¬ ( A ∨ B ) ⇔ (¬ A ∧ ¬ B )
Not A or B is true if and only if not A and not B is true
Not A or B is false if and only if not A and not B is false
Distributive Law
The other law that I found useful was the distributive law which is similar to expansion of polynomials in Advanced Functions.
The one concept which I found difficult was trying to figure out which implications imply each other, and determining if the implications are true both ways or one way. Although our class is done taking up questions like this, I'm still trying to understand, and go through problems in case its on the final exam. I think the problem with these certain questions, is that I can't seem to come up with examples. For instance, in Assignment 1 question number 5 I found it difficult to find a counterexample that made one part False and the other True, and even an example that made both True. Luckily in this case my partner helped me understand this question, but nevertheless I really want to understand these types of problems and make it a goal to understand them for the upcoming weeks.
De Morgan's Law
¬ ( A ∧ B ) ⇔ ( ¬A ∨ ¬B )
Not A and B is true if and only if not A or not B true
Not A and B is false if and only if not A or not B is false
¬ ( A ∨ B ) ⇔ (¬ A ∧ ¬ B )
Not A or B is true if and only if not A and not B is true
Not A or B is false if and only if not A and not B is false
Distributive Law
The other law that I found useful was the distributive law which is similar to expansion of polynomials in Advanced Functions.
The one concept which I found difficult was trying to figure out which implications imply each other, and determining if the implications are true both ways or one way. Although our class is done taking up questions like this, I'm still trying to understand, and go through problems in case its on the final exam. I think the problem with these certain questions, is that I can't seem to come up with examples. For instance, in Assignment 1 question number 5 I found it difficult to find a counterexample that made one part False and the other True, and even an example that made both True. Luckily in this case my partner helped me understand this question, but nevertheless I really want to understand these types of problems and make it a goal to understand them for the upcoming weeks.