What constraints would you write to ensure that if $x = 1$ then $y = 0$ where $x, y$ are binary variables?
Until now I only learnt how to build the constraint with 3 binary variables, therefore the difficulty level of this task is very high for me.
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$\begingroup$ cs.stackexchange.com/q/12102/755 $\endgroup$– D.W.Nov 23, 2022 at 9:30
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1 Answer
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Via conjunctive normal form: $$ x \implies \lnot y \\ \lnot x \lor \lnot y \\ (1 - x ) + (1 - y) \ge 1 \\ x + y \le 1 $$
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$\begingroup$ what is the meaning of x + y <= 1 ? @RobPratt $\endgroup$ Nov 23, 2022 at 10:06
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$\begingroup$ @overboxed It is a linear inequality constraint that the binary decision variables $x$ and $y$ are required to satisfy. This constraint prevents $(x,y)=(1,1)$, which is the only solution that would violate the desired implication. $\endgroup$– RobPrattNov 23, 2022 at 13:33