When we convert an automaton to a regular expression, we need to build expression not go through certain other states. Below is a nondeterministic finite automaton with three states. For each of the six orders of the three states, find s for the labels along paths from one state to another state that do regular expressions that give the set of labels along all paths from the first state to the second state that never go through the third state. Then identify one of these expressions from the list of choices below. a) (10)*1 represents the paths from C to B that do not go through A.
b) 1 represents the paths from C to B that do not go through A.
c) (01)+ represents the paths from B to C that do not go through A
d) 1 represents the paths from A to B that do not go through C.

Provided in the explanation section

Explanation:

The below explanation will help to make this question simple to understanding.

For the questions presented, this analysis surfaces,

⇒ a) (10)*1 in this path we can go through A for C to B as 1010 exist from C to A then B also.

i.e. Option A is wrong , there is transition from c to A with 1.

b) 0 represent the path from B to A and from B to C also. So this is also not a solution.

i.e. Option B is wrong with input 1 there is path to both A and B from c

c) (1+11)0)*1 in this path for cover the 1+11 we have to go in two paths one is only 1 and second is 11. So 11 is the path which goes through the A.

i.e. Option c is wrong , with input 0 there is path to c input symbol 1 is not required

d) (01)+ is correct because we have + sign here not * so it not executes multiple times execute only 1 more time. So it is the path from B to C that does not through A.

cheers i hope this helped !!

i think the answer is b.