@manu, no it is not an empty string. Whatever be the common element between L1 and L2 should be removed from L2. Here common element is epsilon.

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a^{n}b^{m}c^{n} here we need to see a and b can be equal but c will also be equal so a^{n} b^{n} can never be exept for n=0 generated by L1

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@Manu

see in, L1 only epsilon is common with L2, because whenever you try to take string containing 'a' in L1, 'c' will also come in that string...but there is no string containing 'c' in L2, so only epsilon in L1 is common with L2,

if m=0, then L1 can generate ab, aabb, aaabbb, and so on.. right?

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if m=0, then it can only generate a^n c^n

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yes, i didn't notice!

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L = L2 - L1 can be written as L2 INTERSECTION L1' COMPLEMENT OF L1 IS DCFL L2 is already DCFL NOW intersection of two dcfl is not closed it means it may or may not be dcfl but here it is dcfl am i right?

$L1= \{a^mb^nc^k\;|\;if\,(m=n)\,then\,(n!=k)\} \\ L2= \{a^ib^jc^k\;|\;if\,(i<j)\,then\,(k<j)\}\\ L3= \{a^ib^jc^k\;|\;(i<j)\,\leftrightarrow \,(k<j)\}$ Could someone please help to conclude the class of above languages? Below mentioned is the logic used to conclude that L1 and L2 are CFL but ... ( i<j) and comp( k<j) ] or [ (i<j) and (k<j) ] = [ (i>=j) and (k>=j) ] or [ ( i<j) and ( k<j) ] = CSL