Week 1: Quantified Sets and Implication

Hello Rod here,

Universal and Existential Quantification
This week in CSC165 was fairly challenging for me. What I had difficulty this week with was understanding the difference between universal and existential quantification. Once I started looking over the examples from lecture and recognizing the keywords that define each claim such as: "all, every, some, exists) and the next step I would take is try to identify what evidence would cause each of these claims to be proven true or falsified. Applying this to the venn diagram was probably the biggest challenge for me. I had a very hard time visualizing whether the sets in the venn diagram would have to be occupied or empty in order to prove the statement false or true. At tutorial this was explained very well and we were quizzed on the exact same problem requiring us to draw a venn diagram showing what evidence will be needed in order to prove or falsify the statement given to us.

Implication
Also we began to look into implication which made sense to me. We looked at a statement in lecture and discussed how the implication has to be true if you are going to verify or falsify the statement. For example:
"If you have blue pants, then you have red hair"
To prove this false you would need to have evidence of someone who has blue pants(satisfies the antecedent) then does not have red hair. You cannot prove this false by saying that someone wearing green pants has purple hair.

Negation
From the last lecture I had a little difficulty understanding what negation does to the statement. How it affects the statement and whether it will still remain true or not. What I am going to do about this is ready over my notes, lecture notes and write out some problems.

Overall it was a good week I learned quite a lot.