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anonymous
 one year ago
is the set of (1,0,1) a closed set under addition, subtraction, and division? why or why not?
anonymous
 one year ago
is the set of (1,0,1) a closed set under addition, subtraction, and division? why or why not?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, it is to addition and multiplication, because if you sum any of the numbers of the set (like 1+0=1, 1+1=0, 0+1=1) you will always get a number that is already in the set. Same with multiplication, ex: 1x0=0 (already in the set), 1x1=1(already in the set), etc But it isn't closed to division or substraction because if you divide 1/0 or 1/0 you dont get a number of the set (indeed is undefined), or 1(1)=2 and 2 isnt in the set.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What if you add \(1\) to \(1\)? Any operation you choose isn't necessarily restricted to only being applied to distinct elements.
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