Set Theory, Basic | Power of a set

Question

Given set A= {a,b}$^3$

What do the formed set look like and what is |A| (cardinility of A)

Answer 1

A={a,b}^3

you can write as A={a,b} {a,b} {a,b}

                           A={(a,a)(a,b)(b,a)(b,b)} {a,b}

                           A= { (a,a,a) (a,a,b) (a,b,a) (a,b,b) (b,a,a) (b,a,b) (b,b,a) (b,b,a) }

 So |A|= 8

But you need to understand difference between Set and Multiset.

In Set, repeated value is count only one time Example- A=  {a,a,b,b,c} which is equal to {a,b,c} but in this question after calculating {a,b}^3 No set will be repeated so |A| is equal to 8

Comments

Thankyou for this explanation 🙂