power set

Question

Comments

 

∑¹ = set of all strings of length 1

     ={0,1,2,3}

∑² = set of all strings of length 2

      =∑.∑ ={0,1,2,3}.{0,1,2,3} = 4*4 = 16 strings of length 2

∑³ = set of all strings of length 3

     =∑.∑.∑ = 16 strings of length 2 * {0,1,2,3} = 64 strings of length 3..

srestha can u plz check this??

Answer 1

Ans 256

it is a power cube set 2⁴ =16

again another power 16⨉16=256

Comments

Sourabh Kumar

∑²=∑$\times$∑

∑²={ (0,0) , (1,1) , (2,2) , (3,3) , (0,1) , (0,2) , (0,3) , (2,0) , (1,0) , (1,2) , (1,3) , (2,1) , (2,3) , (3,0) , (3,1) , (3,2) }

Number of element in ∑² =16

∑³=∑²$\times$∑

and Power set of set ∑ and ∑² both are different.

Let's take a small example

A={1,2}

Power set P(S)={ $\phi$ , {1} , {2} , {1,2} }

and ∑²=∑$\times$∑ = { (1,1) (2,2) , (1,2) , (2,1) }

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@leensharma : according to you sigma^2 contain 16 element and sigma contain 4 element .

then sigma^3=sigma^2 * sigma

                    =16*4=64 the answer will be 64. how it comes 256.

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@srestha then, $\Sigma^{5}$ means repeating same process 4 times.

If, $|\Sigma| = 2$, then $|\Sigma^2| = 2^2 = 4$, $ |\Sigma^3| = 2^4 = 16$ and then $2^{16}$.