The implication of mathematical analysis (?) What the hell does that mean?

in the mathematical analysis, A contains B, which is recorded as:a? B(as a→bin logic), its truth table is as follows:

ABA? Bttttfffttfft

(where T is true,f to false)

Analysis: through the truth table above, we can easily get a few conclusions as follows:

Conclusion 1 If A is F, the B value is T or F, can you get a? B is true.

Conclusion 2 you want a? B is true, just verify that A is t,b f is not present.

In- depth: implication is actually a weaker definition of semantics, a implies B, a contains B, more precisely, a if T then B may be T. That is, the implication is actually a containment relationship, or more exactly a possible domain (perhaps the author's own word, B's possible domain meaning that B is possible, there may be only a possible and impossible two values) of the relationship. Note that A and B may or may not be relevant, and it is not difficult to imagine that the concept of a domain may be more generalized than the inclusion relationship, because the domain may describe a and b related and unrelated situations, and include only for related situations. (So you can say: include the? possible domain). To verify the above two conclusions.

1 A and B are not relevant and can be verified with a possible domain.

A) Verification Conclusion 1:

A: The Sun is playing West (false).

B: Cattle have eight feet (false)/cattle have four feet (true).

It can be seen that the sun is out of the West is a false proposition (all know that the sun is impossible to play West), so can assert a? B (a implies B), because a is a false proposition, the discussion of a? b true or false do not need to look at the value of B, you can think, originally false proposition if it came true, logic chaos, B naturally there may be a true proposition also may be false proposition. It can be said here: If the sun is out in the west, the cow may have eight feet, of course, there may be four feet. (This is really like Discussion 1 | | X, we can see that we don't need to know X, we can assert 1 | | X is true. (Note that we are using a possible concept here.) ）

b) Verification Conclusion 2:

A: The Sun hits the East (true).

B: Cattle have eight feet (false)/cattle have four feet (true).

Here A is the true proposition, see the following expression: If the sun comes out of the East (apparently), the bull is not likely to be eight feet. It's obviously not possible, so you can't get a? B's. Again: If the sun comes out of the East (apparently), the bull is not likely to be four feet (obviously). Obviously, it's possible to get a? B. Can you see that you want a? B, only need to verify the sun hit the East out (true proposition), there will be no false proposition-the cow has eight feet (false proposition) situation. This has been verified.

2 A and B are related, in two cases.

A) Verification Conclusion 1:

This situation can only be judged by the possible domains of unrelated situations, with the same verification conclusion 1, which is not related to a and B above.

b) Verification Conclusion 2:

This situation can be described using the concepts contained, in particular, the inclusion of the relationship can be expressed in a drawing.

A:danny has been to Guangzhou.

B:danny has been to China.

This can be expressed in a picture as follows:

This makes it clear that Danny has been to China's possible domain (where the possible domain value is the circle-containing range) is larger than the possible area where Danny came to Guangzhou. (So you can assert a?) B. ）

And then come to the conclusion 2, is it possible that Danny was not in the circle of China when he came to Guangzhou? Obviously impossible, therefore the conclusion 2 was verified.

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The implication of mathematical analysis (?) What the hell does that mean?