20 Sets and Venn diagrams (Chapter 1)6 Consider the set of real numbersR. Write down the complement of:
a (¡1,0) b [1, 1 ) c [¡ 3 ,2) d (¡ 5 ,7]
e (¡1,1)[[3, 1 ) f [¡ 5 ,0)[(1, 1 )In this section we will explore the number of elements in unions and intersections of sets.Example 5 Self Tutor
Suppose U=fpositive integersg, P=fmultiples of 4 less than 50 g, and
Q=fmultiples of 6 less than 50 g.
a ListPandQ. b Find P\Q. c Find P[Q.
d Verify that n(P[Q)=n(P)+n(Q)¡n(P\Q).a P=f 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , 36 , 40 , 44 , 48 g
Q=f 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 g
b P\Q=f 12 , 24 , 36 , 48 g
c P[Q=f 4 , 6 , 8 , 12 , 16 , 18 , 20 , 24 , 28 , 30 , 32 , 36 , 40 , 42 , 44 , 48 g
d n(P[Q)=16 and n(P)+n(Q)¡n(P\Q)=12+8¡4=
So, n(P[Q)=n(P)+n(Q)¡n(P\Q) is verified.EXERCISE 1E
1 Suppose U=Z+, P=fprime numbers< 25 g, and Q=f 2 , 4 , 5 , 11 , 12 , 15 g.
a ListP. b Find P\Q. c Find P[Q.
d Verify that n(P[Q)=n(P)+n(Q)¡n(P\Q).2 Suppose U=Z+, P=ffactors of 28 g, and Q=ffactors of 40 g.
a ListPandQ. b Find P\Q. c Find P[Q.
d Verify that n(P[Q)=n(P)+n(Q)¡n(P\Q).3 Suppose U=Z+, M=fmultiples of 4 between 30 and 60 g, and
N=fmultiples of 6 between 30 and 60 g.
a ListMandN. b Find M\N. c Find M[N.
d Verify that n(M[N)=n(M)+n(N)¡n(M\N).
4 Suppose U=Z, R=fx 2 Z:¡ 26 x 64 g, and S=fx 2 Z:0 6 x< 7 g.
a ListRandS. b Find R\S. c Find R[S.
d Verify that n(R[S)=n(R)+n(S)¡n(R\S).
5 Suppose U=Z, C=fy 2 Z:¡ 46 y 6 ¡ 1 g, and D=fy 2 Z:¡ 76 y< 0 g.
a ListCandD. b Find C\D. c Find C[D.
d Verify that n(C[D)=n(C)+n(D)¡n(C\D).E Properties of union and intersection
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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_01\020CamAdd_01.cdr Tuesday, 8 April 2014 10:21:01 AM BRIAN