Use good decomposition $($i$.$e$.$ functions with arguments and$/$or return values$)$ to solve the following problems in java.

You may choose how to populate arrays$/$lists with values $($i$.$e$.$ hard$-$coded, randomly generated, read from a file, specified on the command line, or entered interactively. Use sufficient messages so that the program$$s user knows what to do$.$

You may use primitive arrays or ArrayLists. If no data type is specified, you can use any type.

You may implement all the solutions in a single, menu$-$driven client, implement separate solutions in different programs, or group solutions as you see fit.

$1.$ Determine true or false whether an array $($or list$)$ has duplicates. The duplicated values need not be adjacent. Demonstrate your solution on lists with and without duplicates.

$2.$ Determine true or false whether an array $($or list$)$ is sorted in ascending order. Demonstrate your solution on sorted and unsorted lists.

$3.$ From two arrays $($or lists$)$ of the same data type, produce a list containing only those elements that belong to both of the originals.

$4.$ From an array $($or list$)$ of numbers $($either integers or doubles$),$ find the starting index of the longest strictly ascending subsequence. For example, given the array

$\{12,3,7,5,9,8,1,4,10,2\}$

the result is $6,$ since the subsequence $\{1,4,10\}$ starts at index $6$ and is the longest that is strictly increasing. If the list does not have a strictly ascending subsequence $($e$.$g$.$ the list is in descending order$),$ return a negative value.

$5.$ Starting with a String and a single character, produce a list of the indexes in the string where the character occurs. For example, given the string $$bookkeeper$$ and $\text{'}$e$,$ the function would return $\{5,6,8\}$ since $$e$$ occurs at those positions. Return an empty list if the character does not appear in the string at all.