Problem. For a finite set of symbols Î£ the input lists a1, . . . , as and b1, . . . , bs both

only consist of sequences of length 1 with elements from Î£.

Can this version be solved efficiently by an algorithm?

2 / Show that the set {0, 1, 2}âˆ— of all finite 0, 1, 2-sequences is countable. Is the set Nâˆ— = {0, 1, 2, . . .}âˆ— also a countable set?

3/ Prove the following statement by using a diagonal argument:

Let

*be a set. Then there is no surjective map*

**X***f*from

*to the power set*

**X***.*

**P(X)**__Hint__: Consider the subset

**Y âŠ† X with Y := {x âˆˆ X | x /âˆˆ f(x)}**.

Please people try to solve these.. If you have any solution please help me..