•Can anyone please tell in brief:
Natural numbers are closure,commutative,and associative in which operands?
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Answers
Answer:
Addition is the answer dear
Step-by-step explanation:
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Answer:
Closure property
1) Addition: When two natural numbers or whole numbers are added, the result is always a natural number or a whole number. For example, take any two natural numbers, say 3 and 9. Now, 3 + 9 = 12. 12 is a natural/whole number. Therefore, the system is closed under addition.
2) Subtraction: Subtraction of two whole or natural numbers does not always result in a whole number or natural number. For example, take any two natural numbers, say 3 and 9. Now, 3 – 9 = -6. -6 is not a natural/whole number. Therefore, the system is not closed under addition.
3) Multiplication: Multiplication of two whole or natural numbers always results in a whole or natural number. For example, 3 × 9 = 27, 27 is the natural number. Therefore, the system is closed under multiplication.
4) Division: Division of two whole or natural numbers does not always result in whole or natural numbers. For example, 3 ÷ 9 = 1313. 1313 is not a natural number. Therefore, the system is not closed under division.
Commutative Property
It is a property that associates with binary operations or functions like addition, multiplication. Take any two numbers a and b and subtract them. That is a – b, say 5 – (-3). Now subtract a from b. That is b – a, or -3 – 5. Are they same? No, they are not equal. So, the commutative property does not hold for subtraction. Similarly, it does not hold for division too.
Again take any two numbers a and b and add a and b them which comes to a + b. Now add b and a which comes to be b + a. Aren’t the same? Yes, they are equal because of commutative property which says that we can swap the numbers and still we get the same answer.
1) For Addition
a + ( b + c ) = ( a + b ) + c
For example, if we take 2 , 5 , 11
2 + ( 5 + 11 ) = 18 and ( 2 + 5 ) + 11 = 18
2) For Multiplication
a × ( b × c ) = ( a × b ) × c
For example, 2 × ( 5 × 11 ) = 110 and ( 2 × 5 ) × 11 = 110.
Hence associative property is true for addition and multiplication.
3) For Subtraction
Associative property does not hold for subtraction
a – ( b – c ) != ( a – b ) – c
For example, if we take 4, 6, 12
4 – ( 6 – 12 ) and ( 4 – 6 ) – 12
= 4 + 6 = 10 and -2 -=12 = – 14
Therefore associative property is not true for subtraction.
4) For Division
Associative property does not hold for division
a ÷ ( b ÷ c ) != ( a ÷ b ) ÷ c
For example, again if we take 4, 6, 12
4 ÷( 6 ÷12 ) and ( 4 ÷ 6 ) ÷ 12
= 4 ÷ 612612 and 4646 ÷ 12
we get,
= 4 × 2 = 8 and 13×613×6 = 118118
Therefore associative property is not true for division.
Multiplicative Identity for Natural & Whole numbers
The multiplicative identity for natural/whole numbers a is a number b which when multiplied with a, leaves it unchanged, i.e. b is called as the multiplicative identity of any integer a if a× b = a. When we multiply 1 with a natural/whole number a we get
a × 1 = a = 1 × a
So, 1 is the multiplicative identity for natural/whole numbers.
Additive Identity for Natural & Whole numbers
The additive identity for natural/whole numbers a is a number b which when added with a, leaves it unchanged, i.e. b is called as the additive identity of any integer a if a + b = a. Now, when we add 0 with any natural/whole number a we get
a + 0 = a = 0 + a
So, 0 is the additive identity for natural/whole numbers.
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Associative Property
Associative property of integers states that for any three elements(numbers) a, b and c.