Disprove the following: for all non-empty languages A,B,C
(A o B) ⊆ (A o C) → ( B ⊆ C )
In other words, exhibits non-empty languages A, B and C such that B ⊆/ C and ( A o B) ⊆ (A o C)
Thanks
Welcome to the forum. You should know that rule #11 in the sticky thread in each forum section asks to show some effort in solving your problem. To start, is o concatenation?
It is relatively easy to find A, B, C ⊆ {1}* such that A o B = A o C = {1}* and C ⊂ B.