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命题及其关系—1.命题的概念和例子_图文

思考:下面的语句的表述形式有什么 特点?你能判断它们的真假吗? (1)若直线a∥b,则a和b无公共点. (2)2+4=7. (3)垂直于同一条直线的两个平面平行. (4)若x2=1,则x=1. (5)两个全等三角形的面积相等. (6)3能被2整除. 我们把用语言、符号或式子表达的, 可以判断真假的陈述句称为命题. 其中判断为真的语句称为真命题,判断为 假的语句称为假命题. 例1 判断下面的语句是否为命题?若是命题, 指出它的真假。 (1) 空集是任何集合的子集. (2)若整数a是素数,则a是奇数. (3)对于任意的实数a,都有a2+1>0. (4)若平面上两条直线不相交,则这两条直线平 (5)X 行 . 2+x>0. (6)91是素数. (7)指数函数是增函数吗? (8) ( ?2) ? ?2 2 (9)若|x-y|=|a-b|,则x-y=a-b. 例1中的命题(2)(4)(9),具有 “若P, 则q” 的形式 也可写成 “如果P,那么q” 的形式 也可写成 “只要P,就有q” 的形式 通常,我们把这种形式的命题中的P叫做命 题的条件,q叫做结论. 记做: p?q 例2 指出下列命题中的条件p和结论q: (1)若整数a能被2整除,则a是偶数; (2)若四边形是菱形,则它的对角线互相垂直 且平分. 表面上不是“若P, 则q” 的形式,但可以改变 为“若P, 则q” 形式的命题. 思考 “垂直于同一条直线的两个平面平行”。 可以写成“若P, 则q” 的形式吗? 例3 将下列命题改写成“若P,则q”的形式. 并判断真假; (1)面积相等的两个三角形全等; (2)负数的立方是负数; (3)对顶角相等. 练习 1.举出一些命题的例子,并判断它们的真假. 2.判断下列命题的真假: (1)能被6整除的整数一定能被3整除; (2)若一个四边形的四条边相等,则这个四边形 是正方形; (3)二次函数的图象是一条抛物线; (4)两个内角等于 45 的三角形是等腰直角三 角形. ? 3.把下列命题改写成“若P, 则q” 的形 式,并判断它们的真假: (1)等腰三角形的两腰的中线相等; (2)偶函数的图象关于y轴对程; (3)垂直于同一个平面的两个平面平行. 小结. 这节课我们学习了: (1)命题的概念; (2)判断命题的真假; (3)把有些命题改写成“若P,则q”的形式. .

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