Always remember that a language is a set of strings, so yes you can apply set difference property. See Arjun Sir's answer: https://gateoverflow.in/2190/gate2010-17?show=2381#a2381
L1 = RE
L2 = REC
L1-L2 = L1 ∩ L2c = RE ∩ REC = RE ∩ RE = RE
As, REC is closed under complement and RE is closed under intersection.
Why you are using L1 - L2 = L1 ∩ L2 . , why not directly apply SET DIFFERENCE PROPERTY , THAT IS IN CASE OF Recursive enumerable RE- RE = NOT EQUAL TO RE.
Closure Properties of Languages
Is A-B = A∩Bc correct?
Ok , So we cannot take SET DIFFERENCE DIRECTLY , ALWAYS TO USE L1- L2 = L1 ∩ L2c.