Closure Any Property With Example In Wake
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Closure property We can say that rational numbers are closed under addition, subtraction and multiplication. For example: (7/6)+(2/5) = 47/30. (5/6) – (1/3) = 1/2.
Commutative property is applicable only for addition and multiplication processes. Thus, it means we can change the position or swap the numbers when adding or multiplying any two numbers. This is one of the major properties of integers. For example: 1+2 = 2+1 and 2 x 3 = 3 x 2.
Closure property holds for addition and multiplication of whole numbers. Closure property of whole numbers under addition: The sum of any two whole numbers will always be a whole number, i.e. if a and b are any two whole numbers, a + b will be a whole number. Example: 12 + 0 = 12. 9 + 7 = 16.
The closure property for addition of polynomials says that the addition of any polynomials will result in a polynomial. Examples: 1 and x are polynomials, as is their sum: 1+x. x^3 -5 and x+5 are polynomials, as is their sum: (x^3 -5) +(x+5) = x^3 -x.
Closure Property Examples Add-15 + 2 = -13Sum is an integer Subtract -15 - 2 = -17 Difference is an integer Multiply -15 x 2= -30 Product is an integer Divide -15 / 2 = -7.5 Quotient is not an integer
Integers are closed under addition, subtraction and multiplication but not under division.
The set of integers is not closed under the operation of division. because when one intger is divided by another integer,the result is not always an integer. For example, 4 and 9 both are integers, but 4 ÷ 9 = 4/9 is not an integer. Q.
N are closed under exponentiation: for any n,m∈N, nm∈N, where nm is defined as n×n×⋯×n(mtimes). However, this is not true for integers because of the presence of negative numbers: nm need not be in Z even if n,m∈Z.
Closure Property: The closure property of subtraction tells us that when we subtract two Whole Numbers, the result may not always be a whole number. For example, 5 - 9 = -4, the result is not a whole number.
Answer and Explanation: The set of integers is closed for addition, subtraction, and multiplication but not for division.
