Find the two different representations for the following set

Find the two different representations for the following set:
One using abstraction, and other not.

a. {a,b,c}
b. {0,1,5}

Answer :

( a ) The set { a, b , c } is the set that has exactly the elements a , b and c as members. We can present these elements in either order, so

{ a , b , c } = { b , c , a } ; { a , b , c } = { c , a , b } ; { a , b , c } = { c , b , a } or { a , b , c } = { a , c , b } etc.

By abstraction , we can represent

{ a , b , c } = { x : x A where A is the set of all first three english lower case alphabets }

(b)

The set { 0 , 1 , 5 } is the set that has exactly the elements 0 , 1 and 5 as members. We can present these elements in either order, so

{ 0 , 1 , 5 } = { 1 , 5 , 0 } ; { 0 , 1 , 5 } = {0 , 5 , 1 } ; { 0 , 1 , 5 } = { 1 , 0 , 5 } or { 0 , 1 , 5 } = { 5 , 0 , 1 } etc.

By abstraction , we can represent

{ 0 , 1 ,5 } = { x : x = 5m where m = 0 ,1/5 , 1 }