Design Prolog Programs for the following.

Q$1.$ To test whether given numbers are pythagorean triple.

Eg: Input: $?-$is$\_$triple$(3,4,5).$

Output: true

Q$2.$ Find if given numbers are coprime.

Eg: Input: $?-$coprime$(35,64).$

Output: true

Q$3.$ Check whether given numbers form a geometric sequence.

Eg: Input: $?-$is$\_$geometric$\_$sequence$(3,6,12).$

Output: true

Q$4.$ Write a Prolog program that asks the user for their birth year and calculates and prints their age:

Eg: Input: $?-$age

Enter your birth year: $2005$

Output: You are $19$ years old.

Q$5.$ Check a Prolog program that prompts the user to enter their Employee ID and displays their de$-$

partment based on a predefined database. If the entered Employee ID is incorrect $($i$.$e$.,$ not found in

the database$),$ the program should prompt the user to enter the Employee ID again until a valid one

is entered.

Use the following predefined employee database:

$$ Employee ID $123$ belongs to the "manager" department.

$$ Employee ID $324$ belongs to the $"$hr$"$ department.

Eg: Input: $?-$get$\_$dept

Enter your Employee ID: $123$

Output: Your Employee ID is $123$ and you belong to the department:

manager

Input: $?-$get$\_$dept

Enter your Employee ID: $122$

Output: Incorrect Employee id$,$ enter again.

Enter your Employee ID: $123$

Your Employee ID is $123$ and you belong to the department:

manager

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