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 *(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Binary Operation, Abstract Algebra

**Physics Forums | Science Articles, Homework Help, Discussion**