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wwws1377com:高中数学人教A版选修2-1练习课件:1.1.2 四种命题_图文

第一章 常用逻辑用语 1.1 命题及其关系 课时作业2 四种命题 1 课堂对点训练 2 课后提升训练 [目标导航] 1.了解四种命题的概念. 2.认识四种命题的结构,会对命题进行转换. 课堂对点训练 知识点一 四种命题的概念 1.已知a,b,c∈R,命题“若a+b+c=3,则a2+b2 +c2≥3”的否命题是( ) A.若a+b+c≠3,则a2+b2+c2<3 B.若a+b+c=3,则a2+b2+c2<3 C.若a+b+c≠3,则a2+b2+c2≥3 D.若a2+b2+c2≥3,则a+b+c=3 解析:a+b+c=3的否定是a+b+c≠3,a2+b2+c2≥3 的否定是a2+b2+c2<3. 答案:A 2.若命题A的逆命题是B,命题A的否命题为C,则B 是C的( ) B.否命题 D.以上都不正确 A.逆命题 C.逆否命题 命题的否命题互为逆否命题. 解析:由四种命题之间的关系知原命题的逆命题与原 答案:C 3.命题“若a>b,则2a>2b-1”的否命题为 __________. 解析:“a>b”的否定是“a≤b”,“2a>2b-1”的否 定是“2a≤2b-1”. 答案:若a≤b,则2a≤2b-1 知识点二 四种命题的真假 4. 命题“若a> b ,则ac2> bc 2( a , b, c ∈ R)”与它的逆 命题、否命题、逆否命题中,真命题的个数为( A.0 B.2 ) C.3 D.4 解析:原命题“若a>b,则ac2>bc2(a,b,c∈R)”为 假命题;逆命题“若ac2>bc2,则a>b(a,b,c∈R)”为真 命题;否命题“若a≤b,则ac2≤bc2(a,b,c∈R)”为真命 题;逆否命题“若ac2≤bc2,则a≤b(a,b,c∈R)”为假命 题. 答案:B 5 .分别写出下列命题的逆命题、否命题、逆否命 题,并判断其真假: (1)矩形的对角线相等且互相平分; (2)正偶数不是质数. 解: (1) 逆命题:若一个四边形的对角线相等且互相 平分,则它是矩形.(真命题) 否命题:若一个四边形不是矩形,则它的对角线不 相等或不互相平分.(真命题) 逆否命题:若一个四边形的对角线不相等或不互相 平分,则它不是矩形.(真命题) (2) 逆命题:如果一个正数不是质数,那么这个正数 是偶数.(假命题) 否命题:如果一个正数不是偶数,那么这个数是质 数.(假命题) 逆否命题:如果一个正数是质数,那么这个数不是 偶数.(假命题) 课后提升训练 温馨提示:请点击按扭进入WORD文档作业

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