1. Write the following as a set of Prolog predicates:

Eat at the restaurant if it looks nice but if it stinks don't eat there

using:
(a) cut and fail combination
(b) the 'not' predicate.

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2.  Consider the following program which is supposed to insert its first argument, 
a number, into its second argument, a sorted list, giving the third argument 
(also a sorted list):

  insert(X,[H|T],[H|T1]) :- X>H, !, insert(X,T,T1).
  insert(X,L,[X|L]).

   1. Provide an appropriate query to show that this program is incorrect
   2. Change the program so that it works correctly 

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3. Write a ternary predicate delete_all(item,list,result) that is true if result is
obtained from list by deleting all occurrences of item. Use cut to prevent backtracking.
Sample run:

?-delete_all(a,[a,b,c,a,d,a],X).

X=[b,c,d];

No


?-delete_all(a,[b,c,d],X).

X=[b,c,d];

No

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4. Write a binary predicate count_occurrences(input,result) that is true if 'result' is
a list of two-element lists [el, number_of_occurrences_in_input], where 'el' is an element of
the list 'input', and 'number_of_occurrences_in_input' is an integer specifying how many times
'el' occurs in 'input'. For each element 'el' in 'input' there should be a corresponding pair
[el, number_of_occurrences_in_input] in 'result'.
Sample run:

?- count_occurrences([a,b,a,a,b,c],X).

X = [[c, 1], [b, 2], [a, 3]] ;

No

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5. Write a ternary predicate delete_nth that deletes every N'th element from a list. Sample runs:

?- delete_nth([a,b,c,d,e,f],2,L).

L = [a, c, e] ;

No
?- delete_nth([a,b,c,d,e,f],1,L).

L = [] ;

No
?- delete_nth([a,b,c,d,e,f],0,L).

No
?- delete_nth([a,b,c,d,e,f],10,L).

L = [a, b, c, d, e, f] ;

No