ABSTRACT

5401. Find out if the operation * on the set M is associative:

M = N , x ∗ y = x y ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1645.tif"/>

M = N , x ∗ y = gcd ( x , y ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1646.tif"/>

M = N , x ∗ y = 2 x y ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1647.tif"/>

M = Z , x ∗ y = x − y ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1648.tif"/>

M = Z , x ∗ y = x 2 + y 2 ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1649.tif"/>

M = R , x ∗ y = sin x ⋅ sin y ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1650.tif"/>

M = R* , x ∗ y = x ⋅ y x / | x | ? https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1651.tif"/>