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1、1.2充分条件与必要条件 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.教学目标 使学生正确理解充分条件、必要条件和充要条 件三个概念，并能在判断、论证中正确运用 在师生、学生间的交流中
2、增强逻辑思维活动， 为用等价转化思想解决数学问题打下良好的逻 辑基础 教学重点：充分不必要条件、必要不充分条件 的概念； 教学难点：判断命题的充分不必要条件、必要 不充分条件； 课 型：新授课 教学手段：多媒体 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd
3、.Copyright 2004-2011 Aspose Pty Ltd.例5、 用反证法证明：圆的两条 不是直径的相交弦不能互相平分.已知：如图，在O中，弦AB 、CD交于P，且AB、CD不 是直径.求证：弦AB、CD不被P平分.分析：假设弦AB、CD被P平分，连 接OP后，可以推出AB、CD都与OP 垂直，则出现矛盾.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Cli
4、ent Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.证明: 假设弦AB、CD被P平分，由于P 点一定不是圆心O，连接OP，根据垂径定理 的推论，有 OPAB，OPCD ，即过点P有两条直线与OP都 垂直，这与垂线性质矛盾.所以，弦AB、CD不被P平分.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with
5、Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.思考： 1.用反证证法证证明：若函数f(x)在区间间a,b上 是增函数，那么方程f(x)=0在区间间a,b上至 多只有一个实实根.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspos
6、e.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.一般以下几种情况适宜使用反证法（1）结论本身是以否定形式出现的一类 命题；（2）有关结论是以“至多”，或“至少”的 形式出现的一类命题；（3）关于唯一性、存在性的命题；（4）结论的反面比原结论更具体、更容 易研究的命题（正难则反）.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET
7、 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Cl
8、ient Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.4、如果命题“若p则q”为假，则记作p q.3、若命题“若p则q”为真,记作p q(或q p).2、四种命题及相互关系：1、命题：可以判断真假的陈述句，可写成：若p则q. 复 习互 逆原命题 若p则q逆命题 若q则p否命题 若 则逆否命题 若 则互为为 互否 逆 逆否互 否互 否互 逆 Evaluation only.Evaluation only. Created with Aspose.Slides for
9、.NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.判断下列命题是真命题还是假命题： （1）若 ，则 ； （2）若 ，则 ； （3）对角线互相垂直的四边形是菱形； （5）若 ，则 ； （4）若方程 有两个不等的实数解， 则 真 假 假 假 真 方程有 两个不等的实数解(6) 若两三角形全等 ，则两三角形面积相等；真两三
10、角形全等 两三角形面积相等Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.定义：充分条件与必要条件：一般地，如果已知 ， 即命题“若p则q” 为真命题，那么就说，p 是q 的充分条件， q
11、 是p 的必要条件两三角形全等是两三角形面积相等的充分条件两三角形面积相等是两三角形全等的必要条件两三角形全等 两三角形面积相等Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例1 指出下
12、列各组命题中，p是q的什么条件，q是p的什么条件.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.定义：对于命题“若p则q”Evaluation only.Evaluation only.
13、 Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例2、以“充分不必要条件”、“必要不充分条件”、“充 要条件”与”既不充分也不必要条件“中选出适当的一种 填空. （充分不必要条件）（充分不必要条件） （必要不充分条件）（必要不充分条件）（充要条件）（充
14、要条件）（既不充分也不必要条件）Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.BAEvaluation only.Evaluation only. Created with Aspose
15、.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.DBEvaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slid
16、es for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例7、若p是r的充分不必要条件，r是q的必要 条件，r又是s的充要条件，q是s的必要条件. 则：1）s是p的什么条件？2）r是q的什么条件？必要不充分条件充要条件Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 C
