I have the following statement:
($G$ is a set of some n by n matrices and $I$ is the identity matrix) For every $A \in G$, there exists a $B \in G$ such that $AB=BA=I$.
I want to negate the statement. Here is my answer:
There exists some $A\in G$, for every $B\in G$, $AB \neq BA$ or $BA\neq I$.
But my lecturer marked me wrong. Here is the answer given by him:
There exists some $A\in G$, for every $B\in G$, $AB \neq I$ or $BA\neq I$.
There is also another answer, which is the following:
There exists some $A\in G$, for every $B\in G$, $AB \neq BA$ or $BA\neq I$ or $AB\neq I$.
Which one of the above three is correct? I am confused now. Thanks very much.
All the answers are equivalent .You should talk to your teacher , he graded to fast.