第一章1.1.3第2课时1.(2014·湖北高考)已知全集U={1,2,3,4,5,6,7},集合A={1,3,5,6},则∁UA=()A.{1,3,5,6}B.{2,3,7}C.{2,4,7}D.{2,5,7}解析:∵全集U={1,2,3,4,5,6,7},集合A={1,3,5,6},∴∁UA={2,4,7}.答案:C2.(2013·湖北高考)已知全集U={1,2,3,4,5},集合A={1,2},B={2,3,4},则B∩(∁UA)=()A.{2}B.{3,4}C.{1,4,5}D.{2,3,4,5}解析:∵U={1,2,3,4,5},A={1,2},∴∁UA={3,4,5},∴B∩∁UA={2,3,4}∩{3,4,5}={3,4}.答案:B3.设全集U=R,集合A={x|x≥1},B={x|0≤x≤2},则∁U(A∩B)是()A.{x|1≤x≤2}B.{x|0≤x≤1}C.{x|x>2或x<1}D.{x|0≤x<1}解析:∵A∩B={x|1≤x≤2},∴∁U(A∩B)={x|x>2或x<1}.答案:C4.设集合S={三角形},A={直角三角形},则∁SA=____________.答案:{锐角三角形或钝角三角形}5.设集合U={1,2,3,4,5},A={2,4},B={3,4,5},C={3,4},则(A∪B)∩(∁UC)=________.解析:A∪B={2,3,4,5},∁UC={1,2,5},故(A∪B)∩(∁UC)={2,5}.答案:{2,5}6.设U=R,A={x|a≤x≤b},∁UA={x|x<3或x>4},求a,b的值.解:∵A={x|a≤x≤b},∴∁UA={x|x<a或x>b},又∁UA={x|x<3或x>4},∴a=3,b=4.1