白马非马

韓非子是战国法家, 荀子的高徒, 秦始皇宰相李斯的同学。他说"白马非马", 即白马不是马, 可以用集合論(Set Theory) 证明:

Let 马 = H = {w, b, r, y ...}
w : 白马
b : 黑马
r ：红马
y：黄马

Let 白马 = W = {w}

To prove:
H = W
We must prove:
H ⊂ W and H ⊃ W

From definition we know:
$latex w \in H \supset W $
$latex H \nsubseteq W $
$latex \implies H \neq W $

白马≠马
白马非马
[QED]

其他例子:
木魚非鱼

Solution Birthday

Be careful of the sequence of dialogues which lead to correct sequence of eliminations.

Dialogue 1: (by red color)

Ben says: I do not  know which month (M), also sure that  Mark does not know which date (N)

=> they are both confused by duplicate M & N

=> eliminate unique dates N: 7/6, 1/12

Ben infers that not in M = 6, 12

 => eliminate 4/6 , 1/12, 8/12 (duplicate Month M)

Dialogue 2: (by Blue color)

Mark says: Initially I don't know, now I know (N)

=> eliminate duplicate dates N : 5/3, 5/9

Dialogue 3: (by yellow)

Ben says: now I also know (which month M)

=> eliminate duplicate month M: 4/3, 8/3

Remain the answer: 1/9 

[QED]

Logic Puzzle: Birthday

Logic: Monkey's Dilemma

西遊记 (The Journey to the West)

On the way to the West, the team came to a Y-junction, either go Left or Right.
The Monkey King (孙悟空 ) went out reconnaissance, only came back few days later.
The Pig (猪八戒) suspects this fellow is a monster in disguise of the monkey, may not tell the truth.
The smart Monk (三藏) asks only 2 questions to detect his identity :

Q1. Is 'Left' direction correct ?
Q2. If I ask you Q1, you would say "Yes", would-you?

The true Monkey will answer "Yes/Yes" or "No/No", regardless the correct direction.
Why ?

Case 1. If the Correct direction =Left

Monkey: (Q1, Q2) = (Y,Y)
Monster (tell lie) = (N,Y)

Case 2. If the Correct direction =Right

Monkey : =(N,N)
Monster (tell lie) =(Y, N)

Logic: Pascal Wager

Pascal Wager:

1. We can choose to believe God exists, or we can choose not to so believe.
2. If we reject God and act accordingly, we risk everlasting agony and torment if He does exist (Type I error in Statistics lingo) but enjoy fleeting earthly delights if He doesn't exist.
3. If we accept God and act accordingly, we risk little if He doesn't exist (Type II error) but enjoy endless heavenly bliss if He does exist.
4. It's in our self-interest to accept God's existence.
5. Therefore God exists!

Mathematical Proof:
Pascal assumed
Probability of God exists = p
Probability God doesn't exist = 1-p

You lead 2 lives, either Worldly (世俗) or Piously （虔,诚) , you get rewards X, Y, infinity or Z, as shown in table below.

In Worldly Life, the Expectation in probability is

Ew = p.X + (1-p).Y

In pious life, the Expectation is

Ep = p.∞  + (1-p).Z

Regardless how big the rewards in X (negative, punishment by God) ,Y, Z (self-sacrifice, negative reward)

Ep is infinitely bigger than Ew.

(Ew is good only if p= 0)

Conclusion: no matter what, pious life is better.