For each statement below, decide whether it is true or false. If it is true, justify your answer. If it is not true, give a counterexample. All parts refer to languages over {0,1}. a. If L1 ⊆ L2, and L1 cannot be recognized by a FSA, then L2 cannot. b. If L1 ⊆ L2, and L2 cannot be recognized by a FSA, then L1 cannot. c. If L1 cannot be recognized by a FSA, then L1c cannot. Note: L1c is the complement of L1. d. If neither L1 nor L2 can be recognized by a FSA, then L1 ∪ L2 cannot. e. If neither ?1 nor ?2 can be recognized by a FSA, then ?1 ∩ ?2 cannot.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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For each statement below, decide whether it is true or false. If it is true, justify your
answer. If it is not true, give a counterexample. All parts refer to languages over {0,1}.
a. If L1 ⊆ L2, and L1 cannot be recognized by a FSA, then L2 cannot.
b. If L1 ⊆ L2, and L2 cannot be recognized by a FSA, then L1 cannot.
c. If L1 cannot be recognized by a FSA, then L1c cannot. Note: L1c is the complement of L1.
d. If neither L1 nor L2 can be recognized by a FSA, then L1 ∪ L2 cannot.
e. If neither ?1 nor ?2 can be recognized by a FSA, then ?1 ∩ ?2 cannot.
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