Question

Take a set of natural numbers from 1 to 20 as a universal set
X = {x | x € n , 1 < x < 15}
Y = {y | y € n , 7 < y < 15}

Answer 1

Answer :

X = { 2 , 3 , 4 , . . . , 14 }

Y = { 8 , 9 , 10 , . . . , 14 }

Note :

★ Methods of representing a set :

1. Roster / Tabular / Listed form

2. Set Builder form

★ Roster form :

• All elements are listed .

• Elements are separated by commas .

• Elements are enclosed within braces { } .

• The elements are not repeated .

★ Set builder form :

• The common properties of elements are written .

• The element is described using symbols like x , y , z .

• Whole description of elements are enclosed within braces { } .

★ Universal set :

• Any set which is superset of all the sets under consideration or discussion , then it is called universal set .

• It is denoted by U or μ or S or Ω .

Solution :

The given Universal set :

μ = set of natural numbers from 1 to 20 .

μ = { 1 , 2 , 3 , . . . , 20 }

The given sets in set builder form are :

X = {x | x € n , 1 < x < 15}

Y = {y | y € n , 7 < y < 15}

The set X in roster form will be :

X = { 2 , 3 , 4 , . . . , 14 }

The set Y in roster form will be :

Y = { 8 , 9 , 10 , . . . , 14 }

Hence ,

X = { 2 , 3 , 4 , . . . , 14 }

Y = { 8 , 9 , 10 , . . . , 14 }