目的:通过复习及对交集与并集性质的剖析,使学生对概念有更深刻的理解
设全集 U = {1,2,3,4,5,6,7,8},A = {3,4,5} B = {4,7,8}
求:(CU A)∩(CU B), (CU A)∪(CU B), CU(A∪B), CU (A∩B)
解:CU A = {1,2,6,7,8} CU B = {1,2,3,5,6}
(CU A)∪(CU B) = {1,2,3,5,6,7,8}
A∪B = {3,4,5,7,8} A∩B = {4}
CU (A∩B) = {1,2,3,5,6,7,8,}
二、另外几个性质:A∩A = A, A∩φ= φ, A∩B = B∩A,
A∪A = A, A∪φ= A , A∪B = B∪A.
进而讨论 (x,y) 可以看作直线上的点的坐标A∩B 是两直线交点或二元一次方程组的解,同样设 A = {x | x2-x-6 = 0} B = {x | x2+x-12 = 0}
则 (x2-x-6)(x2+x-12) = 0 的解相当于 A∪B
即: A = {3,-2} B = {-4,3} 则 A∪B = {-4,-2,3}
四、关于集合中元素的个数
作图 观察、分析得:
card (A∪B) ¹ card (A) +card(B)
card (A∪B) = card (A) +card (B) -card (A∩B)
五、(机动):《课课练》 P8 课时5 "基础训练"、"例题推荐"