Click here to watch ALL problems on real-numbersQuestion 174659: which of the complying with sets is closed under division?a. Nonzero whole numbers b. Nonzero integersc. Nonzero even integersd. Nonzero rational numbers discovered 2 solutions by Edwin McCravy, Mathtut:Answer through Edwin McCravy(18851) (Show Source): You have the right to put this systems on her website! i beg your pardon of the adhering to sets is closeup of the door under division?a. Nonzero entirety numbers No, it"s not closed since it"s possible to divide our means out that the collection of entirety numbers. For instance we have the right to start v two nonzero entirety numbers, to speak 5 and also 2, and also divide them and get 2.5, i beg your pardon is not a totality number. So us have separated our way out that the collection of entirety numbers. Since this is possible, the set ofnonzero whole numbers is not closed under division.
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b. Nonzero integersNo, it"s no closed, because that non-zero entirety numbers space nonzero integers, and the over example mirrors that it"s not closed. c. Nonzero even integersNo since it"s possible to division our method out the the set ofnonzero also integers. For instance we deserve to start with two nonzeroeven integers, speak 8 and also 6, and divide them and also get , whichis no a nonzero also integer. So us have split our method out of theset that nonzero even integers. Because this is possible, the collection ofnonzero also integers is not closed under division.d. Nonzero reasonable numbersYes due to the fact that it is difficult to division our way out that the set ofnonzero rational numbers. For instance we can start through two nonzerorational numbers, to speak and , i m sorry is undoubtedly a nonzero rational number. So us cannot division our way out the the collection of nonzero rational numbers. Because this is not possible, the set of nonzero rational number is undoubtedly closed under division.Edwin prize by Mathtut(3670) (Show Source): You can put this solution on her website! d) is the answer:Rational numbers space closed under addition, subtraction, multiplication, as well as division by a nonzero rational.A set of facets is close up door under an procedure if, once you use the procedure to elements of the set, you constantly get another element that the set.
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For example, the totality numbers are closed under addition, since if you add two entirety numbers, you constantly get an additional whole number - over there is no way to gain anything else. But the whole numbers are _not_ closed under subtraction, due to the fact that you deserve to subtract two entirety numbers to gain something that is not a whole number, e.g., 2 - 5 = -3