which of the following properties hold for subtraction of whole numbers?
A. Closure property
B. Associative property
C. commutative property
D. identity property
Oh, subtraction is a bit of a tricky one when it comes to these properties. Let me break it down for you:
A. Closure property: Nope, subtraction doesn't have closure because when you subtract two whole numbers, you may end up with a result that is not a whole number. For example, 5 minus 7 gives you -2. Negative numbers are not part of the set of whole numbers.
B. Associative property: Nah, subtraction isn't associative either. Changing the grouping of the numbers being subtracted will definitely give you different results. Like (10 - 5) - 3 is not the same as 10 - (5 - 3).
C. Commutative property: Ding ding ding! Finally, we have a winner! Subtraction is indeed commutative. You can switch the order of the numbers being subtracted and still get the same result. So 7 - 3 is the same as 3 - 7. Isn't that nice?
D. Identity property: Nope, subtraction doesn't have an identity element like addition does with zero. If you subtract zero from any whole number, you get that same number back, but it's not considered an identity property.
So, the answer is C. Commutative property. Keep in mind that subtraction likes to keep things interesting with its limited properties.
The properties that hold for subtraction of whole numbers are:
A. Closure property: Subtraction of two whole numbers will always result in a whole number. Therefore, the closure property holds for subtraction of whole numbers.
B. Associative property: Subtraction of whole numbers is not associative. The order of subtraction matters. For example, (4 - 2) - 1 is not equal to 4 - (2 - 1).
C. Commutative property: Subtraction of whole numbers is not commutative. Switching the order of subtraction will result in different answers. For example, 4 - 2 is not equal to 2 - 4.
D. Identity property: The identity property of subtraction states that subtracting zero from any number does not change the value of that number. For example, 5 - 0 is equal to 5. Therefore, the identity property holds for subtraction of whole numbers.
So, the properties that hold for subtraction of whole numbers are:
A. Closure property
D. Identity property
To determine which of the properties hold for subtraction of whole numbers, let's first understand what each property means:
1. Closure property: This property states that when you perform an operation on two whole numbers, the result will also be a whole number.
2. Associative property: This property refers to the grouping of numbers when performing an operation. For example, if you have three whole numbers a, b, and c, the associative property states that (a - b) - c is equal to a - (b - c).
3. Commutative property: This property states that the order of the numbers does not matter when performing an operation. For example, for any two whole numbers a and b, a - b is equal to b - a.
4. Identity property: This property states that there is a specific whole number, called the identity element, which when added (or subtracted) to any whole number, does not change its value. For addition, the identity element is 0, and for subtraction, the identity element is the same number itself.
Now, let's apply these properties to subtraction:
A. Closure property: Subtraction of whole numbers does not hold the closure property. For example, if you subtract 5 from 3, the result is -2, which is not a whole number.
B. Associative property: Subtraction of whole numbers does hold the associative property. For example, (5 - 3) - 2 is equal to 5 - (3 - 2).
C. Commutative property: Subtraction of whole numbers does not hold the commutative property. For example, 5 - 3 is not equal to 3 - 5.
D. Identity property: Subtraction of whole numbers does not hold the identity property. When subtracting a whole number from itself, the result is always 0, not the original number.
Based on this analysis, the only property that holds for subtraction of whole numbers is the associative property (option B).
There is clearly no associative nor communative property of subtraction
a-(B-c)clearly does not equal (a-b)-c
nor does
a-b=b-a
The closure property: Depends on the set you are defining, for instance, subtraction of real numbers, example 5-7=-2 is closed, as 5, 7, and -2 are all real numbers. However, if the set is defined as natural numbers, then -2 is NOT a natural number, so the property of closure of subtraction of natural numbers does not exist. So this property may or may not hold, it depends on set definition.
So now, identity propery. The identity property for addition is that if you add zero to any number, the number is unchanged. The subtraction identity is that if you subtract zero from any number, it is unchanged.