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- Write a C-program to read marks in the Programming and DataStructure Laboratory (out of 100) for N (to be read before) students.Consider the interval of marks 0-5, 6-10, 11-15, and so on. Note thatthe first interval contains 6 numbers, and other intervals are of 5numbers. Find the interval of marks having maximum number ofstudents in the class and compute the difference between its centerpoint from the mean of the distribution of marks.Provide results for the following inputs:1. N=2045, 56, 60, 15, 80, 90, 12, 85, 35, 58,63, 73, 52, 78, 47, 23, 14, 58, 18, 962. N=3054, 65, 6, 51, 8, 9, 21, 58, 53, 85,36, 37, 25, 87, 19, 93, 44, 85, 17, 69,40, 0, 3, 33, 16, 63, 95, 69, 74, 38Let Q(x) be the statement “x hasn’t developed a program in JAVA”, where the domain consist of the students in ICS. Express each quantifications in English statement. 1.) ƎxQ(x) 2.) ¬ƎxQ(x) 3.) Ǝx¬Q(x)(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.
- The language we are using here is in Racket. Please try tying each of the following (car '(11 12 13 14)) (car '(a b c d)) (cdr '(11 12 13 14)) (cdr '(a b c d)) (car (11 12 13 14)) (cdr (a b c d)) What do car and cdr do? That last line of the above should cause an error. Explain why the single quote necessary and what it does.Write a program in C to find out a fuzzy set B in Y using the extension principle for r >= 3 You may extend to: r = 3, and the function is the sum of 3 squares.For any program P that takes as input a string, can P ever solve a language other than Y(P)? If your answer is yes, give an example. If your answer is no, briefly justify your answer
- A finite sequence of symbols from a given alphabet will be called a string over the alphabet. A string that consists of a sequence a1, a2, a3, a4, … … … … , an of symbols will be denoted by the juxtaposition a1 a2 a3 a4 … … … … an. Given the strings: u = a2bab2and v = bab2, Evaluate the following operations for strings: (i) ԑu(ii) u + v(iii) u(u| v)(iv) v | (v | u)create a 2 tape Turing machine (use JFLAP) that has on tape 1 the alphabet of a,b,null, on tape 2 the alphabet is 0,1,2,3, null. Tape 1 has initial content of (a+b)*, Tape 2 has initial content of (0+1)* Begin by processing tape 1, if the substring aa is found on tape 1, search tape 2 for the first 00 substring and replace it with 22 if the substring bb is found on tape 1, search tape 2 for the first 11 substring and replace it with 33. If at anytime aa does not have a matching 00 reject if at anytime bb does not have a matching 11 reject else accept after all of tape 1 has been processed.Define a recursive function (rem r b) that, given a regular expression r and a bool b, returns a new regular expression r′ that matches exactly the set of all strings s such that string bs is matched by r. We will call r′ the remainder of r after division by b. For example, if r matches {T,FF T,TFF} and b = T, then r′ can be any regular expression that matches exactly the set {ε,FF} (because T and TFF are the only strings matched by r that begin with b = T, and their remainders are ε and FF, respectively). Here are some examples of what your function could output (but these are not the only answers!): • rem (false(false+true)∗) false = (false+true)∗ • rem (false(false+true)∗) true = ∅• rem (false∗ + true∗) true = true∗• rem ((false∗)(true∗)) true = true∗ Your implementation need not output these exact regular expressions as long as it always outputs an equivalent regular expression (i.e., one that matches the same set of strings as the given answer). These are also not the only test…
- Extend the JML definition of Peano from the lecture with a function computing the minimum of two numbers.Hint 1: This is Peano, and you cannot check something like '<' yet.Hint 2: You could define ≤ (geq) as follows: (a) geq(0,x) = true, (b) geq(s(x),0) = false, (c) geq(s(x),s(y))=geq(x,y).Hint 3: You could define min as follows: (a) min(0,x) = 0, (b) min(x,0) = 0, (c) min(s(x),s(y))=s(min(x,y)).Computer Science Suppose L ⊆{a, b}∗ is defined as follows: Λ∈L; for every x and y in L, the strings axb, bxa, and x yare in L. Show that L =AEqB , the language of all strings x in {a, b}∗ satisfying n_a (x) =n_b (x).for C++ write a progam for the greatest common divisor of integers x and y is the largest integer that evenly divides both x and y. Write a recursive function gcd that returns the greatest common divisor of x and y. The gcd of x and y is defined recursively as follows. If y is 0 the answer is x; otherwise gcd(x, y) is gcd(y, x%y).