Define the following Prolog predicates:

(a) increasing(List) which is true if List is a monotonically increasing list of numbers (e. g. [1,1,3,4,5,5,5,7])

(b) decreasing(List) which is true if List is a monotonically decreasing list of numbers (e. g. [7,7,5,5,3,2,1,1]

(c) sorted(List) which is true if List is sorted (increasingly or decreasingly)

(d) analyze(List) which displays the message ‘This list is sorted’, or ‘This list is not sorted’ depending on the values in the list.

(e) minplusmax(List, MinPlusMax) which returns the sum of the minimum and the maximum element of the List

Notes: (1) Performance of these predicates is not critical (all reasonable solutions are OK); (2) monotonically increasing means that each value is less than or equal to the next value ; (3) in definitions of new predicates, you may use your previously defined predicates.