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To show addition is a binary operation on the set of negative Irrational numbers.

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It's not the case. -√2 and -5+√2 are both irrational negative numbers, but their sum is -5, which is rational.
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I haven't seen the set symbol I before, are you 100% positive it's for irrational numbers? Because if it is, the statements is simply false, as the other comment demonstrated
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This question is from highschool first year so I don't know they would give such a question. I'm thinking maybe there is an easier way to do this.

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