$(2.10$pts$)$ Computational problem solving: Problem specification

Problem Definition: Suppose you are asked to develop AI software to solve the problem of

placing $8$ chess queens on an $8\backslash$times $8$ chessboard so that no two queens attack each other.

Specify the problem to a level of detail that would allow you to develop solution strategies

and corresponding algorithms. State the problem specification in terms of $(1)$ inputs, $(2)$ dis$-$

crete structures for data representation, and $(3)$ desired outputs. No need to discuss so$-$

lution strategies. You must use discrete structures $($e$.$g$.,$ sets, arrays, relations, functions,

sequences, propositional logic, predicates, logical operators, and quantifiers$).$ Each chess

queen has a position defined by a row and column number in the range $[1,8].$ So$,$ a position is

defined as a pair of row and column numbers. The row and column numbers cannot be outside

the range of the chessboard. You need to determine the input representation, the representa$-$

tion of the solution, and constraints that specify acceptable$/$valid solutions $($e$.$g$.,$ what does it

mean for two chess queens not to be threats to each other and how can these conditions be

defined by logical and mathematical constraints imposed on their positions?$)$