- #1

s3a

- 818

- 8

1. Homework Statement

1. Homework Statement

(Theory of Computation) proof problem about proving that L = L(A) by proving that L ⊆ L(A) and that L(A) ⊆ L:

https://www.docdroid.net/du7lLvh/theproblemanditssolution.pdf

## Homework Equations

• Mutual simple induction

• Formal usage of transition function of DFAs (meaning knowing how to use the delta notation)

• Potentially, proof by contrapositive

• Knowing that A = B can be proven by proving A ⊆ B and B ⊆ A.

## The Attempt at a Solution

My question is: does the "δ̂(p, w) = p ⇒ w has even number of 1's" from second part (L ⊆ L(A)) need the first part (L(A) ⊆ L) to already be shown, or is it completely independent, such that the second part (L ⊆ L(A)) could have been cut and pasted, verbatim, before the first part (L(A) ⊆ L)?

Any input would be GREATLY appreciated!