命题“若(x-1)(x-2)=0,则x=1或x=2”的否命题是A.若(x-1)(x-2)≠0,则x≠1且x≠2B.若(x-1)(x-2)≠0,则x≠1或x≠2C.若(x-1)(x-2)=0,则x≠1且x≠2D.若(x-1)(x-2)≠0,则x=1且x=2
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A
解析分析:若p则q命题的否定要注意对p和q同时否定,还要注意x=1或x=2的否定为x≠1且x≠2.
解答:(x-1)(x-2)=0的否定为(x-1)(x-2)≠0,??? ?x=1或x=2的否定为“x≠1且x≠2”.???? 即命题“若(x-1)(x-2)=0,则x=1或x=2”的否命题是:“若(x-1)(x-2)≠0,则x≠1且x≠2”???? 故选A
点评:本题考查了若p则q命题的否定,属于基础题.