Click right here to see ALL difficulties on real-numbersQuestion 174659: i beg your pardon of the adhering to sets is closeup of the door under division?a. Nonzero whole numbers b. Nonzero integersc. Nonzero even integersd. Nonzero rational numbers found 2 options by Edwin McCravy, Mathtut:Answer through Edwin McCravy(18875) (Show Source): You can put this equipment on your website! which of the complying with sets is closeup of the door under division?a. Nonzero entirety numbers

**No, it"s not closed because it"s possible to divide our means out of the set of totality numbers. For instance we have the right to start v two nonzero whole numbers, say 5 and 2, and divide them and also get 2.5, i beg your pardon is not a entirety number. So us have divided our means out of the collection of whole numbers. Due to the fact that this is possible, the set ofnonzero entirety numbers is not closed under division.**

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b. Nonzero integers

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**No, it"s not closed, because that non-zero entirety numbers are nonzero integers, and the above example mirrors that it"s not closed.**c. Nonzero also integers

**No since it"s feasible to divide our method out the the collection ofnonzero even integers. For instance we can start v two nonzeroeven integers, to speak 8 and 6, and also divide them and also get , whichis not a nonzero also integer. So we have split our means out that theset that nonzero even integers. Because this is possible, the collection ofnonzero even integers is not closed under division.**d. Nonzero reasonable numbersYes due to the fact that it is difficult to divide our method out the the set ofnonzero rational numbers. For example we can start through two nonzerorational numbers, to speak and , i m sorry is without doubt a nonzero rational number. So we cannot division our means out the the set of nonzero rational numbers. Due to the fact that this is not possible, the set of nonzero rational number is undoubtedly closed under division.Edwin price by Mathtut(3670) (Show Source): You can put this solution on her website! d) is the answer:Rational numbers are closed under addition, subtraction, multiplication, as well as division by a nonzero rational.A set of elements is close up door under an operation if, once you apply the procedure to aspects of the set, you constantly get another element of the set.

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Because that example, the entirety numbers space closed under addition, since if you include two entirety numbers, you constantly get one more whole number - over there is no method to gain anything else. But the whole numbers space _not_ closed under subtraction, due to the fact that you have the right to subtract two entirety numbers to obtain something that is no a whole number, e.g., 2 - 5 = -3