Prove that a language is regular I'm working on an example which says that a string x is obtained from a string w by deleting symbols if it is possible
to remove zero or more symbols from w so that just the string x remains. For example, the
following strings can all be obtained from 0110 by deleting symbols:

λ, 0, 1, 00, 01, 10, 11, 010, 011, 110, and 0110.

Let Σ = {0, 1} and let A ⊆ Σ
∗ be an arbitrarily chosen regular language. 

Define
B = {x ∈ Σ
∗
| there exists a string w ∈ A such that x is obtained from w by deleting symbols}.

In words, a string is in B if you can obtain that string by first choosing a string from A and
then deleting zero or more symbols from that chosen string. Prove that B is regular.

I'm not able to prove it. Any help would be appreciated.
Hint 1: As $A$ is regular, it is recognized by finite automata. Try to modify this automata to make it recognize $B$.

Hint 2: Skipping "deleted" symbols might be handled by adding $\epsilon$ - transitions to the original automata in a proper way.