complement of (0+1)*

Question

What will be the complement of (0+1)*...Is it {}=ϕ  or  {ϕ}.

And also what is the difference between the two?

Comments

complement of (0+1)* is {} ---> means no element and is represented as phi

But {phi} --> it means there's one element --> this is not empty set rather set conating an element phi.

Answer 1

The complement of (0+1)*.= $\sum$ ^* - (a+b)^*  =ϕ   = { }

What is the meaning of { phi }  set contain one element which is phi , 

What is the meaning of { } = phi = set does not contain any element . IN TOC {phi } = phi  but in Discrete math they have diffrent meaning.

Comments

why in toc set changes its behaviour sir ?

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@anirudh...Many times i came across the term { } but  not {ϕ} (set containing ϕ) What is the significance of this set ?

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power set of {phi } = {{},{phi}}

power set of {}= {phi} only

http://math.stackexchange.com/questions/209063/is-the-empty-set-a-power-set

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{ϕ} is just like a folder has only an empty folder.

So the first folder is not empty i,e. {ϕ} not equal to ϕ

but other is empty.