Truth table
φ ∧ ψ = ψ ∧ φ
∧ conjunction 合取: anyone is false, φ ∧ ψ will be false
∨ disjunction 析取: anyone is truth, φ ∨ ψ will be truth.
∨ : Communism, Soviet Union, China, Socialism, anyone is truth, then it is truth, Big, resources absorbing power, Totalitarianism
∧ : Germany,
Greek alphabet - Wikipedia
φ: phi
ψ: psi
θ: Theta
Quiz
True table game, triary logic
(φ ∧ ψ) ∧ θ = φ ∧ (ψ ∧ θ)
| φ | T | T | F | F |
|---|---|---|---|---|
| ψ | T | F(1) | T(2) | F |
| φ ∧ ψ | T | F(1) | F(2) | F |
| ψ | T | T(2) | F(1) | F |
| θ | T | F(2) | T(1) | F |
| ψ ∧ θ | T | F | F | F |
| (φ ∧ ψ) ∧ θ | T | F(1) | F(2) | F |
| φ ∧ (ψ ∧ θ) | T | F | F | F |
When calculate triary logic , mark a number(1 or 2) in each block , and must always track the same number for each calculation.
eg. (φ ∧ ψ) ∧ θ = (φ ∧ ψ)F(1) ∧ θT(1) = F(1)
(φ ∨ ψ) ∨ θ = φ ∨ (ψ ∨ θ)
(φ ∨ ψ) ∧ θ = (φ ∧ θ) ∨ (ψ ∧ θ)
(φ ∧ ψ) ∨ θ = (φ ∧ θ) ∨ (ψ ∧ θ)
Vocabulary
Caculus 微积分
integers 整数
rational numbers (fractions) 有理数（分数）?
real numbers 实数
arbitrary real number 任意实数?
the property
ambiguously precisely
the most important reason for using language precisely is more advanced parts of mathematics? ****Advanced mathematics is very abstract, and language is the only means we have to access it and decide what is true and what is false.
1. Ambiguous sentences
1.1 Each subscriber to a newspaper in Washington, DC.
1.1.1 Each subscriber to a newspaper published in Washington, DC.
1.1.2 Each newspaper subscriber who lives in Washington, DC.
1.2 John saw Jane driving down the street.
1.2.1 John, while driving down the street, saw Jane.
1.2.2 John saw Jane, who was driving down the street.
1.3 The man saw the woman with a telescope.
1.3.1 The man saw the woman who with a telescope.
1.3.2 The man with a telescope saw the woman.
2. Ambiguous Newspaper headlines
(a) Sisters reunited after ten years in checkout line at Safeway.
a.1 Sisters used to meet in checkout line at Safeway, then ten years passed by, they Reunited in somewhere else.
a.2 Sisters used to meet in somewhere else, then ten years passed by, they Reunited in checkout line at Safeway.
(b) Large hole appears in High Street. City authorities are looking into it.
b.1 ~, City authorities are looking into the hole.
b.2 ~, City authorities are looking into the High street.
(c) Mayor says bus passengers should be belted.
c.1 ~, there are no belts on the bus right now.
c.2 ~, there are belts on the bus right now.
3. No head injury is too trivial to ignore.
3.1 Except Head injury, the other kinds of patients could not be ignored.
3.2 Head injury is too trivial to ignore, NO! nothing special or serious, it could be ignored.
4. In case of fire, do not use elevator
4.1 Do not use elevator, during a fire.
4.2 Do not use elevator, it might cause the fire.
5. This page intentionally left blank
5.1 The pages after this one are intentionally left blank.
Tips: Even This page is not blank, because this one sentence.
6. Writer not intended
without the context, the writer will be misunderstood.
Windows is the best Operating System
Bill gates: Windows is the best Operating System, affordable for Super Maria Game players before 2000.
Examples produced by GPT.
6.1 Example from “The Guardian,” November 29, 2019:
- Sentence: “The man hit the nail on the head, and it was a real headache.”
- Intended Meaning: The man accurately identified a problem or solution, which caused relief.
- Literal Misinterpretation: The man physically struck a nail with his head, resulting in a headache.
6.2 Example from “The New York Times,” March 14, 2018:
- Sentence: “The chef who murdered his wife finally received his just desserts.”
- Intended Meaning: The chef who committed a crime against his wife faced the appropriate consequences.
- Literal Misinterpretation: The chef who killed his spouse was served a dessert as a form of punishment.
6.3 Example from “CNN,” May 5, 2020:
- Sentence: “Scientists discovered a new strain of bacteria in the hospital, raising concerns among patients.”
- Intended Meaning: The discovery of the new bacteria strain in the hospital worried patients.
- Literal Misinterpretation: Scientists found a new type of bacteria growing in the hospital, physically raising it, causing concern among patients.
7. Comment on the sentence “The temperature is hot today.”
using appropriate scientific terminologies, properties and values to express the weather or climate precisely
The temperature is about 35 degrees Celsius in the middle noon, weather is hot today.
8. N = (p1 ·p2 ·p3 · … ·$p_n$)+1, $p_n$ is is prime, prove not every N is prime.
N = 2·3·5·7·8·9 + 1 = 15121
JUST FOR FUN
1. “and” occurs five times in succession.
A billionaire who inherited rich oil inheritance has 72 wives and countless children and grandchildren that he cannot name them. Whenever a large family gathering is held, he always sits on the super luxurious Bentley wheelchair inlaid with gold, he pointed at two children each time with his only two movable fingers, muttering incoherently: and, and, and, and… to let the children came to receive gifts on a big table filled with precious stones . As for why he had 72 wives? The number of children he has is uncontrollable. According to his belief, only man who go to heaven deserve this auspicious number.
一个继承了丰厚石油遗产的亿万富翁，拥有72位妻子以及数不清子孙后代，以至于他无法叫出孩子们的名字。每当举行大型家庭聚会时，他总是坐在一把镶嵌着黄金的超豪华宾利轮椅上，用唯一可动的两根手指，每次指着两个孩子，嘟哝着：**和，和，和，和……，**让孩子们走到他的桌子前领取装满珍贵宝石的礼物。
为什么他要娶72位妻子？以至于无法控制孩子的数量。根据他的信仰，只有进入天堂的男人，才配得上72这个吉祥数字。
2. and, or, and, or, and occur in that order, with no other word between them.
Among Python logical operators, you often use and, or, and, or, and.
Daniel Damerau: Several companies with ambiguous abbreviations, like AND, OR and OR, and some others are obviously unknown to the general population.