This week proved to be very productive, not only was I able to complete my exercise before the due date, but I was able to obtain help of implication issue; thanks Danny that comment & office hour was tremendously helpful and I now feel I have a strong chance in tackling implications.
We started this week off with the Vacuous Truth to present the rule "iff P is False or Q is True" does the implication evaluate to true or sometimes called "vacuously true" when P is False from the start. I found this to be quite straight-forward. However, the next topic Equivalence was quite confusing, where
"Every male employees earn between 25000 and 45000"
was presented. This was the area I didn't quite understand, I believe the class' answer was False, but I evaluated this to be True... I plan to get help with this tomorrow (but for those reading this I wouldn't mind a comment). On the other hand I believe I understood
"For all x belonging to Real, x^2 - 2x + 2 = 0 <=> x > x + 5"
... since the left is False the forward direction is True, and since the right is False the converse is True making an equivalence.
The last slide over this week that presented me trouble was Symbolic Idiom/Restricting Domains, I didn't understand the difference between,
"For all x belonging to D, P(x) => Q(x)" and "For all x belonging to D, P(x) ^ Q(x)"
But overall, this third week went relatively well and I look forward to the fourth week.
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AFter Al quits, I think the set of male employees, and those earning [25000,45000] is the same.
ReplyDeleteFor the restricted domains, the implication is true when P(x) is false, but the conjunction is not.