which operation does not follow to closure property for intesers
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the divison operation does not follow closure property for integers
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HEY MATE!!!!
HERE IS UR ANS________
___________ ↪a/b + c/d = (ad+bc)/bd, so closed under addition.
a/b - c/d = (ad-bc)/bd, so closed under subtraction.
a/b * c/d = (ac)/(bd), so closed under multiplication.
a/b / c/d = (ad)/(bc), so closed under division.
Wait!! but what if bc = 0?
b cannot be zero, because a/b is rational. But, c can be 0, so bc might be zero, and if so, then (ad)/(bc) is not rational, so
NOT closed under division, unless you add "except for division by zero".
Wait!! but what if bd = 0 in the first three examples for addition, subtraction, and multiplication? That is impossible, because you are given that a/b and c/d are rational.
HERE IS UR ANS________
___________ ↪a/b + c/d = (ad+bc)/bd, so closed under addition.
a/b - c/d = (ad-bc)/bd, so closed under subtraction.
a/b * c/d = (ac)/(bd), so closed under multiplication.
a/b / c/d = (ad)/(bc), so closed under division.
Wait!! but what if bc = 0?
b cannot be zero, because a/b is rational. But, c can be 0, so bc might be zero, and if so, then (ad)/(bc) is not rational, so
NOT closed under division, unless you add "except for division by zero".
Wait!! but what if bd = 0 in the first three examples for addition, subtraction, and multiplication? That is impossible, because you are given that a/b and c/d are rational.
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