Help please? I am not sure how to do these. Much appreciated!

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

You are working as a security analyst in a company xyz that owns the whole subnet range of 23.0.0.0/8 and 192.168.0.0/8. while monitoring the data, you find a high number of outbound connections. you see that ip's owned by xyz (internal) and private ip's are communicating to a single public ip. therefore, the internal ip's are sending data to the public ip. after further analysis, you find out that this public ip is a blacklisted ip, and the internal communicating devices are compromised. what kind of attack does the above scenario depict?

When running anti-virus software , what could be a reason where recipitent is not guaranteed that data being streamed will not get interrupted?