Set Theory

Tabular (Roster) Form and Set-Builder Form

Example-1-

Write the solution set of the equation x2+x-2=0.

Solution-

x2-x+2x-2=0

x(x-1)+ 2(x-1)=0

(x-1)(x+2)=0

x=1 , x= – 2

S={1, -2}

Example-2-

Write the set {x: x is a positive integer and  x2<40}

Solution-

S={1, 2, 3, 4, 5, 6}

7, 8, 9, 10, ………… can not be included because their squares are greater than 40.

Example-3- 

Write the set   A={1, 4, 9, 16, 25, 36, ………..} in set builder form.

Solution-

S={x: x is square of a natural number}

You can also write the set as

S={x: x=n2, where n ∈ N}

Example-4-

Write the set {1⁄2,  2⁄3, 3⁄4, 4⁄5, ……………………} in the set-builder form.

Solution-

S={x: x=n⁄(n+1), where n∈ N and 1<=n<=6}.

 

To see the explanation watch the video.

 

 

 

 

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