Ex 3.1, 3

Transcript

Ex 3.1, 3 We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer Closure is when an operation (eg: "adding") on members of a set (eg: natural numbers) always makes a member of the same set. Which means If two Natural numbers are added, the result is also a natural number. So, it means that Natural number is closed under Addition Let’s do both addition and subtraction of Natural numbers and check if they are closed Adding Natural numbers Natural numbers are numbers starting from 1, like 1, 2, 3, 4, 5, … Adding any two natural numbers 5 + 100 = 105 Here, 105 is a natural number Similarly, 10 + 1 = 11 Here, 11 is a natural number Since on adding Natural numbers, the result is also a Natural Number, we can say that Natural Numbers are closed under Addition Subtracting Natural numbers Natural numbers are numbers starting from 1, like 1, 2, 3, 4, 5, … Subtracting any two natural numbers 100 – 5 = 95 Here, 95 is a natural number And, 3 – 6 = –3 Here, –3 is not a natural number Similarly, 1 – 10 = –9 Here, –2 is not a natural number Since on subtracting Natural numbers, the result is not always a Natural Number, we can say that Natural Numbers are NOT closed under Subtraction