Sets (Chapter 2) 59THE COMPLEMENT OF A SET
Suppose U=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 g and A=f 2 , 4 , 5 , 7 , 8 gThe set of elementsf 1 , 3 , 6 gincludes all elements ofUthat arenotelements ofA. We call this set the
complementofA, and denote itA^0.
No element ofAis inA^0 , and no element ofA^0 is inA.ThecomplementofAis the set of all elements ofUwhich arenotelements ofA.
We denote the complementA^0.EXERCISE 2A
1 U=f 1 , 2 , 3 , 4 , 5 , ......, 12 g, S=f 2 , 4 , 7 , 9 , 11 g and T=f 4 , 11 g.
a Find: i n(U) ii n(S) iii n(T):
b List the setsS^0 andT^0.
c True or false? i SμU ii SμT
d True or false? i 52 S ii 52 =T
e If R=f 4 , 7 , 11 , 9 ,xg and SμR, findx.
f IsSfinite or infinite? Explain your answer.2 The subsets offa,bgare?, fag, fbgand fa,bg.
a List all subsets offag.
b List all subsets offa,b,cg.
c Predict the number of subsets offa,b,c,dgwithout listing them.3 List all proper subsets of S=f 2 , 4 , 7 , 9 g.
4 List the elements of the setSwhich contains the:
a factors of 6 b multiples of 6
c factors of 17 d multiples of 17
e prime numbers less than 20
f composite numbers between 10 and 30 :5 Find n(S) for each set in 4.6 Suppose A=fprime numbers between 20 and 30 g, B=feven numbers between 20 and 30 g,
C=fcomposite numbers between 20 and 30 g, and D=fmultiples of 18 between 20 and 30 g.
a List the elements of each set.
b Find: i n(A) ii n(D).
c Which of the sets listed are:
i subsets ofA ii proper subsets ofC?
d True or false? i 232 C ii 272 =A iii 252 B7aSuppose U=f 2 , 3 , 4 , 5 , 6 , 7 , 8 g, A=f 2 , 3 , 4 , 7 g, and B=f 2 , 5 g. Find:
i n(U) ii n(A) iii n(A^0 ) iv n(B) v n(B^0 )
b Copy and complete: For any set SμU whenUis the universal set, n(S)+n(S^0 )=::::::Prime numbers have
exactly two factors.
Composite numbers have
more than 2 factors.iii T½SIGCSE01
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Y:\HAESE\IGCSE01\IG01_02\059IGCSE01_02.CDR Monday, 15 September 2008 12:04:47 PM PETER