finite automata – Regular language is closed given transposition of rightmost character to leftmost

This answer assumes that the transposed language never contains the empty string.

Let $L$ be a regular language, say accepted by a DFA with states $Q$, initial state $q_0$, accepting states $F$, and transition function $delta$.

We construct a new DFA with states $Q’ = q’_0 cup (Q times Sigma)$. The initial state of the new DFA is $q’_0$. The transition function is defined as follows: $delta'(q’_0,sigma) = (q_0,sigma)$, and $delta'((q,sigma),tau) = (delta(q,tau),sigma)$. Finally, the set of accepting states $F’$ contains all states $(q,sigma)$ such that $delta(q,sigma) in F$.

The new DFA reads the first symbol $sigma$ and remembers it. It then simulates the original DFA, accepting a word if adding $sigma$ would result in the original DFA accepting it.

Abstract Algebra True or False [closed]

Hope you are all well,

Im posting this on behalf of a friend and her first language is not english, i will relay any help given to her however im not familiar with the math formulas and terms, however she can comprehend the math side of it, and anything she needs help understanding i will do my best to assist.

Below she has provided images of her answers and working out, she would like confirmation for her given answers and the working out, there are 8 questions in total.

question 7 Img

Also, if you could be kind enough to help on the following question also which she is struggling with.

Question 8 Img

Any Help on this would be greatly appreciated!
Many Thanks In Advance!

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nikon – Recovering a video file that was never closed properly?

The situation has happened a few times now. My Camera a Nikon d5600 will occasionally give me a message about the battery not being being a Nikon battery and shut down the power. (It is an OEM Nikon battery) and another time when I was plugged in with the camera and accidentally pulled the plug. Anyway power went off in the middle of shooting a time lapse and the file was lost.

So I have looked around at recovery software and it seems all the stuff I can find is for recovering deleted files. While there maybe something that works to recover a file that was not deleted but not saved properly, I cannot find it with the free stuff. I don’t mind paying for software but it is not clear if the software will work in my situation and I don’t want to put cash out for a none solution. If you have been able to recover a file in this kind of situation I would appreciate knowing the software you used. I hate to be picky about an answer but if you have not actually had and fixed this particular problem you might be mudding the solution with conjecture.