How to remodel this analytic if-then constraint? – or.stackexchange.com retort

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How to remodel this analytic if-then constraint? – or.stackexchange.com

assume the binary variables $x, y, z in {0,1}$.
I’d affection to formulate the 2 if-then constraints:
$$ x + y geq 2 implies z = 0, tag{1} $$
$$ x + y leq 1 implies z = 1. tag{2} $$
Constraint …

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