Equivalence class toc made easy

Question

How comes 3 states i got 4 states

Comments

But its not a minimal dfa

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You don't need to draw DFA for this problem .
If we see the regEx itself , on expanding.
$R=(a+b)^{*}ba+(a+b)^{*}b+(a+b)^{*}$.

Thus according to the regEx , the language accepted will be all the strings on $\sum^{*}$ concatenated with a 'b' , concatenated with 'a'.

All the strings of $(a+b)^{*}$ will be in either $(a+b)^{*}a$ or $(a+b)^{*}b$ .

So there must be 2 equivalence classes . Right?

But we've forgotten about $\epsilon$ ,since $\epsilon$ is also present in the language .

Thus , there are 3 equivalence classes.

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Hi ,

Can you please explain what do equivalence classes mean?

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So sad to see GATE aspirants going behind such questions. How many grammatical mistakes does this question have? What is meant by "equivalence class" for a regular expression? Do whatever you want but you wont be posting such questions in GO anymore -- "you" means "no one".

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I saw this question in some book too , some study material of some institute.

@ajayjain024 https://en.wikipedia.org/wiki/Equivalence_class

Equivalence relation is required to define equivalence classes , here in this question i think they wanted to ask what are the different types of strings being represented by regEx and confusing them with equivalence classes.