Show that if the sentence “for all languages L, L _, if L and L ∪ L _ are regular, then L _ is regular” were true, then all languages would be regular.   Are the following true? Prove or give a...


Show that if the sentence “for all languages
L, L_, if
L
and
L

L_ are regular, then
L_ is regular” were true, then all languages would be regular.





Are the following true? Prove or give a counter example.


(a) Each subset of a regular language is regular.


(b) Each regular language has a regular proper subset.


(c) If
L
is regular, then so is {xy
:
x

L, y
_∈
L}.


(d) If
R
is any set of regular languages, then ∪R
is also regular.


(e) The language {wuR
:
u,w

Σ
∗} is regular.








Nov 28, 2021
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