MathematicsWhich of the following options is correct regarding the assertion and reason?Assertion (A): Rational numbers are always closed under division.Reason (R): Division by zero is not defined.

Which of the following options is correct regarding the assertion and reason?


Assertion (A): Rational numbers are always closed under division.


Reason (R): Division by zero is not defined.


  1. A
        A is true and R is the correct explanation of A
  2. B
        A is false and R is false
  3. C
        A is true and R is false
  4. D
        A is false and R is true 

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    Solution:

    Given that, A: Rational numbers are always closed under division.
    Statement A is false as 0 is a rational number because it can be written as 01.
    When we divide any rational number by 0 which is also a rational number, then the resultant number is of the form  m0 where m is any rational number.
    So, the resultant is not defined and hence rational numbers are not closed under division
    Statement R is true,
    Any real number divided by 0 is not defined.
    Therefore, A is false and R is true.
    Hence, option 4 is correct.
     
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