2.4 Give context-free grammars that generate the following languages. In all parts, the alphabet Σ is {0,1}. Aa. {w w contains at least three 1s} b. {w w starts and ends with the same symbol}

Which derivation rule justifies the following argument? If n is a multiple of 4, then n is even. However, n is not even. Therefore, n is not a multiple of 4. O modus ponens O simplification O modus tollens O double negation O De Morgan's Laws

I need the code from start to end with no errors and the explanation for the code ObjectivesJava refresher (including file I/O)Use recursionDescriptionFor this project, you get to write a maze solver. A maze is a two dimensional array of chars. Walls are represented as '#'s and ' ' are empty squares. The maze entrance is always in the first row, second column (and will always be an empty square). There will be zero or more exits along the outside perimeter. To be considered an exit, it must be reachable from the entrance. The entrance is not an exit.Here are some example mazes:mazeA7 9# # ###### # #   ## # # #### #     ## ##### ##       ########## RequirementsWrite a MazeSolver class in Java. This program needs to prompt the user for a maze filename and then explore the maze. Display how many exits were found and the positions (not indices) of the valid exits. Your program can display the valid exits found in any order. See the examples below for exact output requirements. Also, record…

IN PYTHON, Using recursion: ask the user for the length of a square and the character they want to use. Draw the square (similar to mini assignment #15 in functions part 3). Once the user creates the square with their specification, ask them if they want it to be smaller or larger and how many times. Draw all the squares growing in size to the specified range.

Can you help me with this code because this is a little difficult for me:question that i need help with:The Lights Out puzzle consists of an m x n grid of lights, each of which has two states: on and off. The goal of the puzzle is to turn all the lights off, with the caveat that whenever a light is toggled, its neighbors above, below, to the left, and to the right will be toggled as well. If a light along the edge of the board is toggled, then fewer than four other lights will be affected, as the missing neighbors will beignored. In this section, you will investigate the behavior of Lights Out puzzles of various sizes by implementing a LightsOutPuzzle class task: A natural representation for this puzzle is a two-dimensional list of Boolean values, where True corresponds to the on state and False corresponds to the off state. In the LightsOutPuzzle class, write an initialization method __init__(self, board) that stores an input board of this form for future use. Also write a method…

Keeping data structures and algorithms in mind, can you help me to write these two functions in java? The factorial of a positive integer n —which we denote as n!—is the product of n and the factorial of n − 1. The factorial of 0 is 1. Write two different recursive methods that each return the factorial of n. Include the two methods in a file called Test.java   What to submit: The Test.java