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Define a binary operation on Z, the set of integers by the equation m * n = m + n + mn. Which of the following statemnts is / are true about the binary structure of Z with *

1) * is not associative

2) There is no element e belonging to Z such that for every z belonging to Z, z*e = e*z = z

3) Property 2) holds but there exists z belonging to Z such that for every y belonging to Z zy does not equal e

A) 1 and 2 only

B) 1 and 3 only

C) 2 only

D) 3 only

E) none of them

Can someone help I have no taken any abstract algebra yet so I am not sure exactly what to do can figure this out please

Well I know associativity means the grouping of addents doesnt matter

i.e (a + b) + c = a ( b + c )

So m *n should be associative then right?

Because m * n = m + n + mn is just adding 3 terms so why shouldnt it be associative.

1) * is not associative

2) There is no element e belonging to Z such that for every z belonging to Z, z*e = e*z = z

3) Property 2) holds but there exists z belonging to Z such that for every y belonging to Z zy does not equal e

A) 1 and 2 only

B) 1 and 3 only

C) 2 only

D) 3 only

E) none of them

Can someone help I have no taken any abstract algebra yet so I am not sure exactly what to do can figure this out please

Well I know associativity means the grouping of addents doesnt matter

i.e (a + b) + c = a ( b + c )

So m *n should be associative then right?

Because m * n = m + n + mn is just adding 3 terms so why shouldnt it be associative.

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