考點(diǎn):命題的真假判斷與應(yīng)用
專(zhuān)題:函數(shù)的性質(zhì)及應(yīng)用,簡(jiǎn)易邏輯
分析:?x∈R,sinx+
≥2,或sinx+
≤-2,可判斷A;?x∈R,
≤1,可判斷B;寫(xiě)出原命題的否定,可判斷C;根據(jù)充要條件的定義,可判斷D.
解答:
解:對(duì)于A(yíng),?x∈R,sinx∈[-1,1],則sinx+
≥2,或sinx+
≤-2,故A錯(cuò)誤;
對(duì)于B,?x∈R,
≤1,故B錯(cuò)誤;
對(duì)于C,命題p:“?x∈R,x
2-x-1>0”的否定¬p:“?x∈R,x
2-x-1≤0”,故C正確;
對(duì)于D,“e
a>e
b”?“a>b”,“l(fā)og
2a>log
2b”?“a>b>0”,故“e
a>e
b”是“l(fā)og
2a>log
2b”的必要不充分條件,故D錯(cuò)誤;
故選:C
點(diǎn)評(píng):本題以命題的真假判斷為載體,考查了全稱(chēng)命題,特稱(chēng)命題,命題的否定,充要條件等知識(shí)點(diǎn),難度不大,屬于基礎(chǔ)題.