Hello I am new here!

Raveena is making a professional presentation for a newly launched product of her company. she wants to incorporate the following features in her presentation. a) to add serial numbers in each slide b) to add name of her company on top of each slide. c) to add the picture of her product on the second slide(the picture of her product is stored on her computer) write the commands/features of her presentation tool using which she can perform the above operations.

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.

The place where the extended axis of the earth would touch the celestial sphere is called the celestial