Question

closure property introduction​

Answer 1

Answer:

a set either has or lacks closure with respect to a given operation. For example, the set of even natural numbers, [2, 4, 6, 8, . . .], is closed with respect to addition because the sum of any two of them is another even natural number, which is also a member of the set.Ap

Step-by-step explanation:

Closure describes the case when the results of a mathematical operation are always defined. For example, in ordinary arithmetic, addition has closure. Whenever one adds two numbers, the answer is a number. ... In the natural numbers, subtraction does not have closure, but in the integers subtraction does have closure.

Answer 2

Answer:

Closure property of addition:

if a and b are two integers, then a+b will also be an integer.

example, 10 + (-9) = +1,

(-8) + 19 = +11,

(-3) + (-3) = -6, all are integers.

Closure property of substraction:

if a and b are two integers, then a - b and b - a both are integers.

example: 2 and (-8) are two integers.

(2) - (-8) = 10 which is an integer.

Similarly, (-8) - (2) = (-8) + (-2) = -10 which is an integer.