State the property of closure of whole numbers. Do all the arithmetic operations follow this property? If not, why? [2 MARKS]
State the property of closure of whole numbers. Do all the arithmetic operations follow this property? If not, why? [2 MARKS]
Property: 1 Mark
Reason: 1 Mark
A set of numbers is said to be closed for a specific mathematical operation if the result obtained when an operation is performed on any two numbers in the set, is itself a member of the set.
Only addition and multiplication operations on whole numbers satisfy the property of closure because when we perform this operation on whole numbers, the result also lies in the set of whole numbers.
But when we perform division on whole numbers, the result may be a whole number or a fraction.
So, it doesn't satisfy the property of closure. Similarly, for subtraction of two whole numbers, the result which we get maybe a positive number or negative number which clearly does not satisfy the property of closure.
Example:-
1) 3 + 4 = 7
Here 3 and 4 are whole numbers.
The addition of 3 and 4 which is 7 is also a whole number.
So, property of closure is true for addition.
(2) 4 - 3 = 1
Here, 4 and 3 are whole numbers and 1 is also a whole number.
So the property is true.
But 3 - 4 = -1
Here 3 and 4 are whole numbers.
The subtraction of 3 and 4 is -1 which is not a whole number.
(3) 1) 30 x 7 = 210
Here 30 and 7 are whole numbers.
The multiplication of 30 and 7 which is 210 is also a whole number.
So property of closure for multiplication is true.
(4) Note : Property of closure is not always true for division.
Example : 45 ÷ 0 = not defined
As division with zero is not possible.
Property: 1 Mark
Reason: 1 Mark
A set of numbers is said to be closed for a specific mathematical operation if the result obtained when an operation is performed on any two numbers in the set, is itself a member of the set.
Only addition and multiplication operations on whole numbers satisfy the property of closure because when we perform this operation on whole numbers, the result also lies in the set of whole numbers.
But when we perform division on whole numbers, the result may be a whole number or a fraction.
So, it doesn't satisfy the property of closure. Similarly, for subtraction of two whole numbers, the result which we get maybe a positive number or negative number which clearly does not satisfy the property of closure.
Example:-
1) 3 + 4 = 7
Here 3 and 4 are whole numbers.
The addition of 3 and 4 which is 7 is also a whole number.
So, property of closure is true for addition.
(2) 4 - 3 = 1
Here, 4 and 3 are whole numbers and 1 is also a whole number.
So the property is true.
But 3 - 4 = -1
Here 3 and 4 are whole numbers.
The subtraction of 3 and 4 is -1 which is not a whole number.
(3) 1) 30 x 7 = 210
Here 30 and 7 are whole numbers.
The multiplication of 30 and 7 which is 210 is also a whole number.
So property of closure for multiplication is true.
(4) Note : Property of closure is not always true for division.
Example : 45 ÷ 0 = not defined
As division with zero is not possible.
