Is the questioner a senior one student? I remember talking about it in the freshman opening collection.

Generally speaking, there is no difference between "harmony" and "harmony".

Yes, there must be something unusual. )

But in some cases, the two cannot be confused. For example, in the example given by the questioner, P and Q are not equivalent.

The reasons are as follows: The P proposition means that f(x) monotonically increases in the interval A, monotonically increases in the interval B and monotonically increases at the junction between the interval A and the interval B. The Q proposition means that f(x) monotonically increases in the interval A and monotonically increases in the interval B..

Draw a picture to illustrate:

For example, in this function, we can only say that the monotone interval of f(x) is (0, 1) and (2,-∞), and we cannot use union. Because f (1) >: f(2).