Question

函數(shù)其中P，M為實(shí)數(shù)集R的兩個(gè)非空子集，又規(guī)定f(P)＝{y|y＝f(x)，x∈P}，f(M)＝{y|y＝f(x)，x∈M}．給出下列四個(gè)判斷：

①若P∩M＝，則f(P)∩f(M)＝；②若P∩M≠，則f(P)∩f(M)≠φ；

③若P∪M＝R，則f(P)∪f(wàn)(M)＝R；④若P∪M≠R，則f(P)∪f(wàn)(M)≠R．

其中正確判斷有

[　　]

A．0個(gè)

B．1個(gè)

C．2個(gè)

D．4個(gè)

Answer 1

答案：A
解析：

若P＝{1}，M＝{－1}則f(P)＝{1}，f(M)＝{1}則f(P)∩f(M)≠故①錯(cuò) 　　若P＝{1，2}，M＝{1}則f(P)＝{1，2}，f(M)＝{1}則f(P)∩f(M)＝故②錯(cuò) 　　若P＝{非負(fù)實(shí)數(shù)}，M＝{負(fù)實(shí)數(shù)}則f(P)＝{非負(fù)實(shí)數(shù)}，f(M)＝{正實(shí)數(shù)}則f(P)∪f(wàn)(M)≠R． 　　故③錯(cuò)．若P＝{非負(fù)實(shí)數(shù)}，M＝{正實(shí)數(shù)}則f(P)＝{非負(fù)實(shí)數(shù)}，f(M)＝{負(fù)實(shí)數(shù)}則f(P)∪f(wàn)(M)＝R．故④錯(cuò)