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所属成套资源:新北师大版数学必修第一册课件PPT全套
北师大版高中数学必修第一册第一章预备知识PPT课件
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这是一份北师大版高中数学必修第一册第一章预备知识PPT课件,文件包含章末总结ppt、132全集与补集ppt、131交集与并集ppt、11集合的概念与表示ppt、12集合的基本关系ppt、31不等式的性质ppt、321基本不等式ppt、43一元二次不等式的应用ppt、211必要条件与充分条件一ppt、4142ppt、221全称量词命题与存在量词命题ppt、222全称量词命题与存在量词命题的否定ppt、212必要条件与充分条件二ppt、322基本不等式的应用ppt等14份课件配套教学资源,其中PPT共417页, 欢迎下载使用。
1.3 集合的基本运算1.3.1 交集与并集知识探究·素养培育探究点一[问题1] 我们知道两个实数除了能比较大小外,还能进行加、减、乘、除等运算,那么两个集合是否也能进行运算呢?如果能,又该如何表示这样的运算?考查下面的各个集合,集合C与集合A,B之间有什么关系?(1)A={2,4,6,8,10},B={3,5,8,12},C={8};(2)A={x|x是甲中学今年在校的女同学},B={x|x是甲中学今年在校的高一年级同学},C={x|x是甲中学今年在校的高一年级女同学}.交集提示:集合C是由那些既属于集合A又属于集合B的所有元素组成的.(1)交集①定义:一般地,由 的所有元素组成的集合,叫作集合A与B的交集,记作 .②符号语言表示为A∩B= .③图形语言表示为 知识点1:交集的概念及运算性质既属于集合A又属于集合BA∩B{x|x∈A,且x∈B}(2)交集的运算性质A∩B B∩AA∩A= .=A⊆B等价于A∩B= .A∩B⊆AA∩B⊆BAA[例1] (1)已知集合M={(x,y)|x+y=2},N={(x,y)|x-y=4},那么M∩N为( )(A){3} (B){-1}(C){3,-1} (D){(3,-1)}(2)设集合A={x|-1≤x≤2},B={x|0≤x≤4},则A∩B等于( )(A){x|0≤x≤2} (B){x|1≤x≤2}(C){x|0≤x≤4} (D){x|1≤x≤4}解析:(2)因为A={x|-1≤x≤2},B={x|0≤x≤4},如图,故A∩B={x|0≤x≤2}.故选A.变式训练1-1:(1)已知集合A={x|x=2n-1,n∈N+},B={x|0≤x≤4,x∈N+},则A∩B等于( )(A){1,2,3,6} (B){1,3}(C){-3,-1,1,3} (D){3}解析:(1)因为集合A={1,3,5,7,…},B=[0,4],所以A∩B={1,3}.故选B.(2)已知集合M={x|-3
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