Zeal Test Series 2019: Theory of Computation - Identify Class Language

Question

in this question L2 is regular  and in first statement what i got that it is

DCFL.COMPLEMENT(DCFL).regular and in 2 one DCFLunion regular 3 i am not getting ,

what i want that can anyone explain the properties of regular with nonregular or anylanguage with regular for this question

Comments

L union REG= L

L intersection REG =L

L - REG= L

here L could be any language(cfl,dcfl,csl, re rec).

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@Ashish what about concatenation and other properties is it true for all

And can you give me the reference from where you have read it

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For other properties you need to check depending upon problem but what i have given you above will always be true.