Mr. Sunil would like to send the following message. How should a telegram to convey this message worded? "Your sales report for July 07 indicates that you have had no sales for T.M. Filing cabinets. Is this really the case or has the figures been omitted by mistakes."
Answers
Explanation:
Closure Property of Addition: a+b=c ⇒ 1+2=3, 7+8=15. This shows that the sum of natural numbers is always a natural number.
Closure Property of Multiplication: a×b=c ⇒ 2×3=6, 7×8=56, etc. This shows that the product of natural numbers is always a natural number.
So, the set of natural numbers, N is closed under addition and multiplication but this is not the case in subtraction and division.
2. Associative Property:
The sum or product of any three natural numbers remains the same even if the grouping of numbers is changed.
Associative Property of Addition: a+(b+c)=(a+b)+c ⇒ 2+(3+1)=2+4=6 and the same result is obtained in (2+3)+1=5+1=6.
Associative Property of Multiplication: a×(b×c)=(a×b)×c ⇒ 2×(3×1)=2×3=6= and the same result is obtained in (a×b)×c=(2×3)×1=6×1=6.
So, the set of natural numbers, N is associative under addition and multiplication but this does not happen in the case of subtraction and division.
3. Commutative Property:
The sum or product of two natural numbers remains the same even after interchanging the order of the numbers. The commutative property of N states that: For all a,b∈N: a+b=b+a and a×b=b×a.
Commutative Property of Addition: a+b=b+a ⇒ 8+9=17 and b+a=9+8=17.
Commutative Property of Multiplication: a×b=b×a ⇒ 8×9=72 and 9×8=72.
So, the set of natural numbers, N is commutative under addition and multiplication but not in the case of subtraction and division.
Let us summarise these three properties of natural numbers in a table. So, the set of natural numbers, N is commutative under addition and multiplication