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Answer 1

Answer:

Collection of all  non zero rational number closed under division

• The rationals are not closed under division because of the possibility of division by zero. Zero is a rational number and division by zero is undefined. It is true that the rationals are closed under division as long as the division is not by 0.

Subtraction is not commutative for rational numbers

• No, unlike addition and multiplication, subtraction is NOT commutative! We know that for any two numbers a and b: a + b = b + a and ab = ba; however, unless a = b, there are an infinite number of examples or cases which illustrate why subtraction does not have a commutative property, i.e., a - b does not equal b - a.

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