Click here to watch ALL difficulties on real-numbersQuestion 174659: which of the adhering to sets is closeup of the door under division?a. Nonzero whole numbers b. Nonzero integersc. Nonzero also integersd. Nonzero reasonable numbers discovered 2 solutions by Edwin McCravy, Mathtut:Answer through Edwin McCravy(18802) (Show Source): You have the right to put this equipment on her website! i m sorry of the adhering to sets is closeup of the door under division?a. Nonzero entirety numbers

**No, it"s no closed due to the fact that it"s feasible to division our way out that the set of whole numbers. For instance we can start v two nonzero whole numbers, speak 5 and 2, and divide them and also get 2.5, which is no a totality number. So we have split our method out of the collection of totality numbers. Due to the fact that this is possible, the collection ofnonzero whole numbers is not closed under division.**

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b. Nonzero integers

You are watching: Is the set of rational numbers closed under division

**No, it"s no closed, for non-zero whole numbers space nonzero integers, and also the above example mirrors that it"s no closed.**c. Nonzero even integers

**No since it"s feasible to divide our means out the the set ofnonzero also integers. For example we deserve to start v two nonzeroeven integers, say 8 and also 6, and divide them and get , whichis no a nonzero even integer. So we have divided our means out of theset that nonzero also integers. Since this is possible, the collection ofnonzero even integers is not closed under division.**d. Nonzero reasonable numbersYes due to the fact that it is impossible to division our means out the the set ofnonzero reasonable numbers. For example we can start v two nonzerorational numbers, to speak and also , i m sorry is certainly a nonzero rational number. So we cannot divide our way out that the collection of nonzero rational numbers. Since this is not possible, the collection of nonzero rational number is indeed closed under division.Edwin answer by Mathtut(3670) (Show Source): You can put this systems on her website! d) is the answer:Rational numbers room closed under addition, subtraction, multiplication, also as division by a nonzero rational.A set of elements is close up door under an procedure if, as soon as you use the procedure to elements of the set, you always get another element that the set.

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For example, the totality numbers space closed under addition, since if you add two entirety numbers, you always get an additional whole number - there is no means to gain anything else. Yet the entirety numbers are _not_ closeup of the door under subtraction, since you have the right to subtract two whole numbers to get something the is no a totality number, e.g., 2 - 5 = -3