PROBLEM 2.1

1.Write down the mathematical notation for:

(a) the set of all even numbers

X=x|x=2y ∀ y∈Z

(b) the set of all natural numbers whose square is less than 21

X=x|x^2 is greater than 21

2.Give a definition of set in Problem.1(b) by means of a list

Set is the collection of well-defined objects.All the objects containing in a set is called as elements. we can represent a set as

{1,2,3,4…..}

3.In each of the following examples say whether the statement x ∈ X is true or false.

(a) x=273,   X={n ∈ N|n is an odd number}

Answer is TRUE

Because an odd number is defined as, 2 multiplied by any number and add one to it which means  (2n+1).so in the case of 273 it can be expressed as 2*(136)+1=273.

(b) x= 273,  X={n ∈ N|n is a prime number}

Answer is FALSE

Because a prime number is defined as, a number which is divided by one and itself only so when we consider 273 ,it can be divisible by 3 which means that the number is not a prime number

(c) x=112279,  X={n ∈ N|n is a perfect square}

Answer is FALSE

Because a perfect square is defined as an integer which is represented by another number with that many number of times .so we can say that 112279 is not a perfect square.

PROBLEM 2.2

1. There are eight different subsets of the set {a,b,c}.Make a list of them.

{a},{b},{c},{a,b},{b,c},{a,c},{a,b,c},null.

PROBLEM 2.3

1.Construct a counter-example for the following statement

for any set A,B,C  A∩(B∪C) = (A∩B)∪C

This is known as distributive property

here  we take A,B,C as each distinct elements which are different.we can solve this property using truth table.