Answer
Verified
394.2k+ views
Hint: Rational numbers are those numbers which can be written in p/q form where p and q do not have common factors and q should not be equal to zero. Closed under division implies that if we divide two rational numbers then the resultant number will also be a rational number.
Complete step-by-step answer:
If we add two rational numbers then the resultant number is also rational which implies rational numbers are closed under addition.
For example- 1 + 2 =3
Here, 1 and 2 both are rational numbers, when we add them the resultant number is 3 which is also a rational number.
If we subtract two rational numbers then the resultant number is also rational which implies rational numbers are closed under subtraction.
For example- 2 - 1 = 1
Here, 1 and 2 both are rational numbers, when we subtract 1 from 2 then the resultant number is 1 which is also a rational number.
If we multiply two rational numbers then the resultant number is also rational which implies rational numbers are closed under multiplication.
For example- 1 * 2 =2
Here, 1 and 2 both are rational numbers, when we multiply them the resultant number is 2 which is also a rational number.
0 is a rational number because it can be written as 0/1. When we divide any rational number by 0 which is also a rational number, then the resultant number is not a rational (infinity is not defined).
Rational number is not closed under division.
Option (B) is correct.
Note:-Rational numbers are closed under division as long as the division is not by zero. Irrational numbers are not closed under addition, subtraction, multiplication or division.
Complete step-by-step answer:
If we add two rational numbers then the resultant number is also rational which implies rational numbers are closed under addition.
For example- 1 + 2 =3
Here, 1 and 2 both are rational numbers, when we add them the resultant number is 3 which is also a rational number.
If we subtract two rational numbers then the resultant number is also rational which implies rational numbers are closed under subtraction.
For example- 2 - 1 = 1
Here, 1 and 2 both are rational numbers, when we subtract 1 from 2 then the resultant number is 1 which is also a rational number.
If we multiply two rational numbers then the resultant number is also rational which implies rational numbers are closed under multiplication.
For example- 1 * 2 =2
Here, 1 and 2 both are rational numbers, when we multiply them the resultant number is 2 which is also a rational number.
0 is a rational number because it can be written as 0/1. When we divide any rational number by 0 which is also a rational number, then the resultant number is not a rational (infinity is not defined).
Rational number is not closed under division.
Option (B) is correct.
Note:-Rational numbers are closed under division as long as the division is not by zero. Irrational numbers are not closed under addition, subtraction, multiplication or division.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE