已知函数f（x）=xlnx，x∈（0，+∞），其导函数为f′（x），现有如下命题：

①对∀x₁∈（0，+∞），∃x₂∈（0，+∞），使得x₂f（x₁）＞x₁f（x₂）；

②对x₁∈（0，+∞），对∀x₂∈（0，+∞）且x₁≠x₂，使得f（x₁）﹣f（x₂）＜x₂﹣x₁；

③当a＞3时，对∀x∈（0，+∞），不等式f（a+x）＜f（a）•e^x恒成立；

④当a＞3时，对∀x∈（3，+∞），且x≠a时，不等式f（x）＞f（a）+f′（a）（x﹣a）恒成立；其中真命题的个数为（   ）

增加：在缺词处加一个漏字符号（∧），并在其下面写出该加的词。

删除：把多余的词用斜线（\）划掉。

修改：在错的词下划一横线，并在该词下面写出修改后的词。

注意：1）每句不超过两个错误；

2）每处错误及其修改均只限一词；

3）只允许修改10处，多者（从第11处起）不计分。

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