I'm reading a wonderful tutorial about neural network. This is the best tutorial I've ever seen but I can't understand one thing as below:

In the link above, it is talking about how the neural work solves the XOR problem.

It says that we need two lines to separate the four points. But I don't know the second tables.

XOR:

input1    input2    output
  0         0         0
  0         1         1
  1         0         1
  1         1         0

First table:

input1    input2    output
  0         0         0
  0         1         1
  1         0         1
  1         1         1

In my opinion, the first table is OK because it includes the XOR, which means that what the second table need to do is to remove the forth input. So I think the second table should be as below:

input1    input2    output
  0         0         1
  0         1         1
  1         0         1
  1         1         0

How in the link it says the second table is like this:

input1    input2    output
  0         0         0
  0         1         0
  1         0         0
  1         1         1

In a word, I can understand why the single layer neural network can't solve the XOR problem but I can't understand how the two layers neural network work to solve it.

I'm reading a wonderful tutorial about neural network. This is the best tutorial I've ever seen but I can't understand one thing as below:

In the link above, it is talking about how the neural work solves the XOR problem.

It says that we need two lines to separate the four points. But I don't know the second table.

XOR:

input1    input2    output
  0         0         0
  0         1         1
  1         0         1
  1         1         0

First table:

input1    input2    output
  0         0         0
  0         1         1
  1         0         1
  1         1         1

In my opinion, the first table is OK because it includes the XOR, which means that what the second table need to do is to remove the forth input. So I think the second table should be as below:

input1    input2    output
  0         0         1
  0         1         1
  1         0         1
  1         1         0

How in the link it says the second table is like this:

input1    input2    output
  0         0         0
  0         1         0
  1         0         0
  1         1         1

In a word, I can understand why the single layer neural network can't solve the XOR problem but I can't understand how the two layers neural network work to solve it.