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# Are the logical expressions returned by Reduce always satisfiable ?

Posted 9 years ago
 Hello everyone, I am trying to solve conjunctions of linear equations together with linear inequalities. As I am looking for a complete solution, and due to the inequalities, I know that the function to use is Reduce. Reduce expresses the complete solution in a logical expression. When the logical expression is simple enough, we can manually verify that it is satisfiable and thus that solution(s) exist(s). But as we can hardly perform such manual verification when the logical expression begins to be too long, the following question arises : when Reduce returns a logical expression different from True or False, is that logical expression always satisfiable ? The fact that I am dealing with linear systems might help. Thanks in advance.
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Posted 9 years ago
 Thank you
Posted 9 years ago
 If I understand your question correctly, the results are always satisfiable. If the input to Reduce is inconsistent, it returns False.
Posted 9 years ago
 My wonder is when Reduce returns an answer different from True or False. For example, when Reduce returns something like this : Can such expressions returned by Reduce be unsatisfiable ? Or are they always satisfiable ?
Posted 9 years ago
 Are the logical expressions returned by Reduce always satisfiable ?
Posted 9 years ago
 If there's no solution, Reduce will return False. In:= eqs = {2 x + 3 y <= 5, x - 2 y >= 1, 1 <= x <= 10, 1 <= y <= 10}; In:= res = Reduce[eqs, {x, y}] Out= False 
Posted 9 years ago
 Are the logical expressions returned by Reduce always satisfiable ?