Consider a rational class designed to represent rational numbers as a pair of ints, along with methods reduce (to reduce the rational to simplest form), gcd (to find the greatest common divisor of two ints), as well as methods for addition, subtraction, multiplication, and division. why should the reduce and gcd methods be declared to be private?

a. because they will never be used
b. because they will only be called from methods inside rational
c. because they will only be called from the constructor of rational
d. because they do not use any of the rationalinstance data
e. this is incorrect; they should be declared as public

Why should characters such as / \ " ' * ; - ? [ ] ( ) ~ ! $ { } < > # @ & | space, tab, and newline be avoided in file names?

Write a program that uses a random number generator to generate a two digit positive integer and allows the user to perform one or more of the following operations: a. double the number. b. reverse the digits of the number. c. raise the number to the power of 2, 3, or 4. d. sum the digits of the number. e. if the number is a two-digit number, then raise the first digit to the power of the second digit. f. if the number is a three-digit number and the last digit is less than or equal to 4, then raise the first two digits to the power of the last digit. after performing an operation if the number is less than 10, add 10 to the number. also, after each operation determine if the number is prime. each successive operation should be performed on the number generated by the last operation. your program should not contain any global variables and each of these operations must be implemented by a separate function. also, your program should be menu driven. 7. (fraction calculator) write a program that

:you areto design the controller for alight that functions both as an ordinary light and also as a motion activated light and alarm. a. if the manual switch s is on, then the light l is on. b. besides the manual switch, there is a motion detector, m1, which activatesthis light. c.if motion is detected but the light is on anyway because s is on, only then a secondoutput a, an alarm, is turned on. d. the disable switch, d, disables the motion activated light and alarmbut leaves manual control operation of the light using switch s.(i)read the problem statement and clearly identify the inputs and outputs for the circuit you are designing. (ii)create the truth table for this system; include the light, alarm, switch, disable, and the motion sensor.(iii)draw a schematic of this system.