This week I had to teach two days in a row, Tuesday and Wednesday, since Presindet's day was on Monday.
I kept talking about propositional logic and quantifiers. The class is 100 minutes long and my intention is to devote most of the class to active learning. I believe me lecturing for about 50 minutes is more than enough.
This week I brought up a problem in showing an equivalence between two propositions involving iff, OR, AND, and negations.
- Students were able to understand the distributive law with the OR and AND connectives
- They also used the identity p∧T = p. They understood how to apply it better when I called it the "happy face" identity 😀∧T = 😀
We also discussed Morgan's laws when using quantifiers. I gave an example of a finite universe (domain) and checked if P(x) was true for every element of U. For example if U={2,3, 5} and P(x) is "x>1", then
P(2) TRUE
P(3) TRUE
P(5) TRUE
In this case, ∀xP(x)=P(2)∧P(3)∧P(5)
If we negate ∀xP(x), we see that the negation of P(2)∧P(3)∧P(5) is one of Morgan's laws discussed in previous classes. This was not a formal proof, but at least it gave a good intuition for Morgan's laws with quantifiers.
Students had fun with the problem where the domain is all people, C(x) is "x is a comedian" and F(x)=" x is funny". They laughed when we said that C(x)∧F(x) means to be a "funny comedian"
We started to work on the example where the domain is all people, P(x) is "x is perfect" and F(x) is "x is my friend"
So, "everyone is perfect" is written ∀xP(x).
I'll ask them to prepare the rest of the statements for the next class.
Overall, I believe students had the opportunity to discuss math during class.
Most importantly... they had fun!
