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Which of the following statements is false.
(a) Addition is commutative for integers
(b) Subtraction is commutative for integers
(c) Integers are closed under addition condition
(d) Integers are closed under subtraction condition
(a) Commutative property for addition
It states that we can add Integers in any order.
For example,
$2+3=3+2=5$
(b) Subtraction of Integers does not follow Commutative property.
For example,
$2-3 = -1$
$3-2 = 1$
$-1 ≠ 1$
Therefore,
$2-3 ≠ 3-2$
(c) Closure property for addition :
Closure property says that if for any two Integers a and b, $a + b$ is also an integer
then the set of integers is closed under addition.
For example,
$3+4 = 7$. Here, all 3,4 and 7 are integers.
(d) Closure property of subtraction :
The difference between any two Integers is always an Integer.
If a and b are any two Integers, then $a - b$ is also an Integer.
For example,
$7-5=2$ is also an Integer.
Therefore, From the above, option (b) is the incorrect option.
Option (b) is false.
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