Monday, Monday

 Today has been gloomy and most of the students arrived a few minutes late. Gloomy... 8 am class. 

We agreed that if the day was not fantastic, we'll make it fantastic! We focus on building valid arguments for quantified statements. Rules of inferences for quantified statements were introduced:

• Universal Instantiation (UI)
• Universal Generalization (UG)
• Existential Instantiation (EI)
• Existential Generalization (EG)

After giving a couple of warm-up examples, we came back to the Socrates example. 

Students are identifying beautifully when to use modus ponens!!!

We then moved on to solve some fun examples. Some students had questions about the inferential rule of Simplification. if we know that the hypothesis is p∧q, should we use p or q as a conclusion?  The answer is...it depends! Which statements are present in the conclusion I want to arrive at? 

We can actually use simplification more than once on different premises. 

Coming attractions: Mathematical proofs.  I mentioned keywords for the next class: 

• Theorem
• Proposition
• Lemma
• Corollary
• Definitions
• Axioms

I'll see you in class!