Cambridge Additional Mathematics

Sets and Venn diagrams (Chapter 1) 19

Example 3 Self Tutor

FindC^0 given that:

a U=fall positive integersg and C=fall even integersg

b C=fx 2 Z:x> 2 g and U=Z

a C^0 =fall odd integersg b C^0 =fx 2 Z:x 61 g

Example 4 Self Tutor

Suppose U=fx 2 Z:¡ 56 x 65 g, A=fx 2 Z:1 6 x 64 g, and

B=fx 2 Z:¡ 36 x< 2 g. List the elements of:

a A b B c A^0 d B^0

e A\B f A[B g A^0 \B h A^0 [B^0

a A=f 1 , 2 , 3 , 4 g b B=f¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 g

c A^0 =f¡ 5 ,¡ 4 ,¡ 3 ,¡ 2 ,¡ 1 , 0 , 5 g d B^0 =f¡ 5 ,¡ 4 , 2 , 3 , 4 , 5 g

e A\B=f 1 g f A[B=f¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 , 2 , 3 , 4 g

g A^0 \B=f¡ 3 ,¡ 2 ,¡ 1 , 0 g h A^0 [B^0 =f¡ 5 ,¡ 4 ,¡ 3 ,¡ 2 ,¡ 1 , 0 , 2 , 3 , 4 , 5 g

EXERCISE 1D

1 Find the complement ofCgiven that:

a U=fletters of the English alphabetg and C=fvowelsg

b U=fintegersg and C=fnegative integersg

c U=Z and C=fx 2 Z:x 6 ¡ 5 g

d U=Q and C=fx 2 Q :x 62 [x> 8 g

2 Suppose U=fx 2 Z:0 6 x 68 g, A=fx 2 Z:2 6 x 67 g, and B=fx 2 Z:5 6 x 68 g.

List the elements of:

a A b A^0 c B d B^0

e A\B f A[B g A\B^0 h A^0 [B^0

3 SupposePandQ^0 are subsets ofU. n(U)=15, n(P)=6, and n(Q^0 )=4. Find:

a n(P^0 ) b n(Q)

4 True or false?

a If n(U)=a and n(A)=b where AμU, then n(A^0 )=b¡a.

b IfQis a subset ofUthen Q^0 =fx 2 U:x= 2 Qg.

5 Suppose U=fx 2 Z:0<x 612 g, A=fx 2 Z:2 6 x 67 g,

B=fx 2 Z:3 6 x 69 g, and C=fx 2 Z:5 6 x 611 g.

List the elements of:

a B^0 b C^0 c A^0 d A\B

e (A\B)^0 f A^0 \C g B^0 [C h (A[C)\B^0

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_01\019CamAdd_01.cdr Tuesday, 19 November 2013 11:54:52 AM GR8GREG