MADE EASY 2022 Work book -Theory of Computation

Question

Which of the following pairs of string belonging to Σ* are distinguishable by the following dfa?

Comments

what exactly “Σ* are distinguishable means” ?

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Two states A and B are distinguishable if there exists some string w belongs to $\sum ^{*}$

such that  $\delta ^{*}(A,w) \in F$ and $\delta ^{*}(B,w) \notin F$.

Then we say A and B are distinguishable by string w.

Now here what is the definition that two strings are distinguishable ?

if we just start with initial state and go with the pair of strings we find both the pairs are either going to final state or both going to non final state.