@Jaideepyadav910
When languages are given don’t go by the general property , check for the given languages.
$S$ : {$a^nb^{n+k}|n≥0,k≥1$} $∪$ {$a^{n+k}b^n|n≥0,k≥3$}
here , considering the first language
$L1$ $=$ {$a^nb^{n}b^{k}|n≥0,k≥1$}
Here there is only one dependency and k is independent of n , it can be written as $a^nb^nb^+$ , clearly $DCFL$.
similarly the other language is also $DCFL$.
Union contains all the Strings from both the set of languages.
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DCFL not closed in Union. Then how?
NOT CLOSED means it may or may not be DCFL.