Please explain the solution


#1

Consider the DFA A given below.

Which of the following are FALSE?

Complement of L(A) is context-free.
L(A)=L((11∗0+0)(0+1)∗0∗1∗)
For the language accepted by A,A is the minimal DFA.
A accepts all strings over {0,1} of length at least 2.
1 and 3 only
2 and 4 only
2 and 3 only
3 and 4 only33


#2

1 is true. L(A) is regular, its complement would also be regular. A regular language is also context free.

2 is true.

3 is false, the DFA can be minimized to two states. Where the second state is final state and we reach second state after a 0.

4 is clearly false as the DFA accepts a single 0.
Source: https://www.geeksforgeeks.org/gate-gate-cs-2013-question-33/