Question

. “Integers does not satisfy the associative property with respect to subtraction”.
Justifyit .

Answer 1

Answer:

18.“Integers does not satisfy the associative property with respect to subtraction justifyit

Answer 2

Answer:

The set of integers with the subtraction operator is an example of a quasigroup.

The integers are closed under subtraction and for all integers a and b, the equations $a - x = b$ and $y - a = b$have unique solutions x and y.However, the structure does not have an identity element (0 is a right identity, but doesn't work as a left identity since 0 a for any a other than 0) and - a hence no inverse elements. Also, subtraction is not associative-in general, $a - (b - c)$ is not equal to $(a - b) - c$Therefore the integers with subtraction is not a loop, semigroup, or any other higher-order structure.Hence,Integers does not satisfy the associative property with respect to Subtraction.

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

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