worksheet 2 - Sets

1.      If A={1,2,3,4,5,6,7,8,9} B={2,3,4,5} C={2,4,6,8} and D={4,5,6,7} find

a.      B U C

b.      B intersection D

c.       (B U C) U (A U D) = A

2.      Which of the following statements are true? Give reasons to support your answer

a.      {0} = empty set

b.      {s,r,t,r}={s,t,r}

c.       If A subset of B then B U A = A

d.      If A subset of B then A intersection (A-B)= empty set

e.      A intersection B = empty set implies A is empty or B is empty

3.      Find the largest and smallest elements of the following sets

a.      A={y: y<=10 , y is an even natural number}

b.      B={t: t is a prime number between 50 and 100}

c.       C= { m: the digits of m add upto to 6, m in N and no digit is zero}

d.      D={n: 3< = 2n <= 40, n leaves remainder 3 when divided by 7}

4.       If D= {y: 1<y<20 and y is a square number} what is n(D)?

5.      If P={p: p is a prime number and 10<= p <= 100} find n(P).

6.      State and prove De morgan’s ;aws on complements.

7.      Given U={x: -3<= x <= 3, x in I} A={-2,0,2} B={0,1,2,3} find the elements of the following sets

a.      A – B

b.      U U B’

c.       (A U B)’

8.      Write the power set of S={2,3}

9.      Given A= {x: x is a letter in the word “ACCUMULATOR”}

a.      Express A in roster form

b.      Find the cardinal number of set of vowels of A

c.       Write down the power set of the set of vowels in A

10.  Write all proper subsets of {0,1,2}

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