Exercise 1.1

1.      If A={1,2,3,4,5}, whether 3,5 and 8 are the members of the set A or not, write with set notation symbols.

Þ 3ÎA, 5ÎA, 8ÏA

2.      A set of odd numbers between 0 and 10. Express it in listing method  and set builder method.

Þ In listing method

      {1,3,5,7,9}

      In set builder method

      {x:xis a odd number, x<10}

3.      If Z= {x:x is an integer, -1£x£1}, express it in description method and listing method.

Þ in description method

     Z is a set of integer more than +ve 1 and less than –ve 1.

     In listing method

     Z= {-1,0,1}

4.      State whether the following sets are null, unit, finite or infinite sets

a)      The set of the highest peak of mountain Þ unit

b)      The set of whole numbers more than 10 Þ infinite

c)      The set of whole numbers between 10 and 100 Þ finite

d)      The set of prime numbers between 14 and 16 Þ null

** Prime numbers are that numbers whose factor is only 1.

5.      If A = {x:x+1£5,xÎW}, find n (A)

Þ here x+1£5

          or,x£5-1

          or, x£4

         i.e A= {0,1,2,3,4}

so n (A) = 5

6.      Whether the sets P = {3,6,9,12} and Q= {1,3,5,7} are equal or equivalent ? Write with reason.

Þ They are equivalent because they have not all same element but same cardinal number.

7.      State whether the sets X = {2,4,6,8} and Y= {6,4,2,8} are equal or equivalent ? Give reason.

Þ They are equal because they have all same elements but just order is different and it have same cardinal number.

8.      State whether the sets A= {a,b,c,d,e} and B= {a,e,i,o,u} are  overlapping or disjoint ? Write with reason.

Þ They are overlapping because they have common elements ‘a’ and ‘e’.

9.      State whether the sets Z= {-2,-1,0,1,2} and N= {3,4,5,6} are overlapping or disjoint ?

Þ They are disjoint because they have no common point.

10. If U= {1,2,3,………15}, A= {1,3,5,7,9}, B= {1,2,3,……15} and C= {4,8,12,16}, answer the following questions.

a.      Is A the subset of U? Give reason.

Þ yes A is the subset of U because U contain every element of A.

b.      Is B the proper subset of U? Give reason.

Þ no because B=A.

c.       Is CÍU? Give reason.

Þ No because one element i.e. 16 is not contained by U.

11. Write the possible subsets of the set A = {3,6,9}

Þ {3},{6},{9},{3,6},{6,9},{3,9},{3,6,9},f

12. What can be the universal sets from which the following subsets can be formed ?

a.      The set of cricket team of a school.Þ the set of student of a school.

b.      The set of literate women of a village.Þ the set of people of a village.

c.       The set of even numbers.Þthe set of natural numbers.