问题 填空题
下列命题中:①∀x∈R,(x-
3
)2>0
;②∀x∈R,ex≥0;③∃x∈Z,61=-3x+2;④∃x∈R,3x2-6x+4=0.其中真命题的个数是______.
答案

∀x∈R,(x-

3
)2>0,此命题不正确,因为当x=
3
时,0>0不成立;

②∀x∈R,ex≥0;,此命题正确,由指数函数的性质知,∀x∈R,ex>0,故一定有 ex≥0;

③∃x∈Z,61=-3x+2,此命题不正确,解方程知,x=

59
3
,不是整数,故此命题不成立;

④∃x∈R,3x2-6x+4=0,此命题不正确,因为此二次方程的判别式小于0,即此方程无实根,故命题错误.

综上,仅有②

故答案为1.

填空题
单项选择题

I want to divide human understanding into two kinds—classical understanding and romantic understanding. In terms of ultimate truth, a distinction of this sort has little meaning, but it is quite legitimate when one is operating within the classic mode used to discover or create a world of underlying form. The terms classical and romantic, as Phaedrus used them, mean the following:
A classical understanding sees the world primarily as underlying form itself. A romantic understanding sees it primarily in terms of immediate appearance. If you were to show an engine or a mechanical drawing or electronic scheme to a romantic, it is unlikely he would see much of interest in it. It has no appeal because the reality he sees is its surface. Dull, complex lists of names, lines and numbers. Nothing interesting. But if you were to show the same blueprint or give the same description to a classical person, he might look at it and then become fascinated by it because he sees that within the lines and shapes and symbols is a tremendous richness of underlying form.
The romantic mode is primarily inspirational, imaginative, creative, intuitive. Feelings rather than facts predominate. "Art" when it is opposed to "Science" is often romantic. It does not proceed by reason or by laws. It proceeds by feeling, intuition and esthetic conscience. In the northern European cultures the romantic mode is usually associated with femininity, but this is certainly not a necessary association.
The classic mode, by contrast, proceeds by reason and by laws—which are themselves underlying forms of thought and behavior. In the European cultures it is primarily a masculine mode and the fields of science, law and medicine are unattractive to women largely for this reason. Although motorcycle riding is romantic, motorcycle repair and maintenance are purely classic. The dirt gives it such a negative romantic appeal that women never go near it.

Only ______ is true to this statement made in Paragraph 3: "Art" when it is opposed to "Science" is often romantic.

A.art is often romantic when it is opposed to science

B.art is often opposed to science when it is romantic

C.art can often be romantic when we clearly define it

D.science is often romantic when it is clearly defined