In the beginning of this week, universal quantification was being discussed and I felt everything was going well. I understood what was written on the slides, what was being taught etc. For example, the ideas of existential & universal quantification, where "Every" would refer to the entire specified set and "Some" or "There is" being at least one within the specified set. I was also able to understand the idea of the Venn diagram, and symbols such as L compliment being the consideration of everything other than those within L. However, all was going well until we entered implications. I understood the examples in the handout/readings of chapter 2, but when it came down to the questions provided in #2 of exercise 1, it completely threw me into a tangent.
What troubled me the most of #2 was how I was suppose to figure out what the antecedent (P) and consequent (Q) is... I attempted to ask for advice from some of my classmates, but the ones I spoke to had issues on this as well. I then went to the CSSU and asked for advice, but they told me there isn't a straight forward way to solving questions like these and said that you had to "reason it out". This didn't exactly aid me in my struggle to figuring out a method of finding P & Q.
I understood the concept of the rule "iff P is False or Q is True" would imply the implication to be true and hence, I was able to figure out #3 without much effort. The rule also applies to #2 as I had already realized for providing a counter example, by showing that P is True and Q is False, and with this I'm currently trying to solve the questions in #2 by attempting to find a counter example. The counter example should allow me to figure out what P and Q are... and hopefully before the due date of this exercise.
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Translating English implications into symbols is tough work. Here is what I recommend.
ReplyDeleteApproach the problem backwards. Think of a counterexample to the implication (if the implication is a rule, what example would break the rule? if the implication is advice, what would it mean to flout the advice?). Once you have a satisfactory counterexample, it must be of the form P-and-not-Q. That allows you to (I hope) read P and Q off directly.