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This in turn gives a solution to the problem of partitioning tri-partite graphs into triangles, [13] which could then be used to find solutions for the special case of SAT known as 3-SAT, [14] which then provides a solution for general Boolean satisfiability. So a polynomial-time solution to Sudoku leads, by a series of mechanical ...
The solution set of a given set of equations or inequalities is the set of all its solutions, a solution being a tuple of values, one for each unknown, that satisfies all the equations or inequalities. If the solution set is empty, then there are no values of the unknowns that satisfy simultaneously all equations and inequalities.
Can you find a problem more general than your problem? Generalization: Induction: Can you solve your problem by deriving a generalization from some examples? Induction: Variation of the Problem: Can you vary or change your problem to create a new problem (or set of problems) whose solution(s) will help you solve your original problem? Search ...
A solution of a polynomial system is a set of values for the x i s which belong to some algebraically closed field extension K of k, and make all equations true. When k is the field of rational numbers , K is generally assumed to be the field of complex numbers , because each solution belongs to a field extension of k , which is isomorphic to a ...
For example, [3] to draw the solution set of x + 3y < 9, one first draws the line with equation x + 3y = 9 as a dotted line, to indicate that the line is not included in the solution set since the inequality is strict. Then, pick a convenient point not on the line, such as (0,0).
In mathematics, the solution set of a system of equations or inequality is the set of all its solutions, that is the values that satisfy all equations and inequalities. [1] Also, the solution set or the truth set of a statement or a predicate is the set of all values that satisfy it. If there is no solution, the solution set is the empty set. [2]
Solution set (portrayed as feasible region) for a sample list of inequations. Similar to equation solving, inequation solving means finding what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an inequation or a conjunction of several inequations.
For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 .