Welcome to my spot! After the first quiz I feel a little stressed, since the logic is harder than it looks.
For visualization with Venn Diagram, sometimes it's sufficient to use only one of ◯ and X; however, in some case excessive usage of ◯ and X can cause wrong answers. To avoid this kind of mistake, I have to be every careful reading through the questions.
For example, to solve this question on quiz,we want to use the diagram to disprove"all students enrolled in a programming course (P)at UofT are also enrolled in a linguistics course (L)at UofT".
What we need is to show "there is some student enrolled in a programming course is not enrolled in a linguistics course".
One little o on the left side of P is sufficient.
For visualization with Venn Diagram, sometimes it's sufficient to use only one of ◯ and X; however, in some case excessive usage of ◯ and X can cause wrong answers. To avoid this kind of mistake, I have to be every careful reading through the questions.For example, to solve this question on quiz,we want to use the diagram to disprove"all students enrolled in a programming course (P)at UofT are also enrolled in a linguistics course (L)at UofT".
What we need is to show "there is some student enrolled in a programming course is not enrolled in a linguistics course".
One little o on the left side of P is sufficient.
In this new lecture, the prof first taught us two new ways to express quantification: using set relations (⊆, ⊈, ∩, ∅, etc.)and using quantifying functions (q1, q2, etc.)Then, we learned the differences between sentences and statements. What interested me most was implication. Many of every language can translate to P => Q, such as "Can’t have P without Q", "P requires Q", "For P to be true, Q must / need to be true", "Not P if not Q."...all of those are saying P is a subset of Q. Suddenly I found some of human language is so redundant. 0.0！
Note:=> does not mean causes
in python functions, return not all means some does not, return not any means NO ONE DOES
Some other things learned:
- for implication, there are converse,contrapositive...
- A Vacuous Truth is a statements that has neither examples nor counterexamples. For example, for any x∈R, x^2 – 2x + 2 = 0 => x > x + 5)
- Equivalence is a statement that satisfies "P => Q" and "P <= Q" simultaneously.That is P IFF Q, P is necessary and sufficient to Q. Also we can make some weird ones by forming Vacuous Truths in both directions.
- Idioms are some expressions, which are utilized more common than others, for restricting domains.
Although I only read the lecture and attended one tutorial, I find myself have big interest in "how to think logically". Also, the mates in tutorial asked questions frequently, which promoted me to think and know better about the material I had missed.
Note:=> does not mean causes
in python functions, return not all means some does not, return not any means NO ONE DOES
Some other things learned:
- for implication, there are converse,contrapositive...
- A Vacuous Truth is a statements that has neither examples nor counterexamples. For example, for any x∈R, x^2 – 2x + 2 = 0 => x > x + 5)
- Equivalence is a statement that satisfies "P => Q" and "P <= Q" simultaneously.That is P IFF Q, P is necessary and sufficient to Q. Also we can make some weird ones by forming Vacuous Truths in both directions.
- Idioms are some expressions, which are utilized more common than others, for restricting domains.
Although I only read the lecture and attended one tutorial, I find myself have big interest in "how to think logically". Also, the mates in tutorial asked questions frequently, which promoted me to think and know better about the material I had missed.
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