Which one of the following in NOT necessarily a property of Group?

consider the binary relation $$R = \left\{ {\left( {x,y} \right),\,\left( {x,z} \right),\,\left( {z,x} \right),\,\left( {z,y} \right)} \right\}$$ on the set $$\left\{ {x,\,y,\,z} \right\}$$. which one of the following is TRUE?

The binary operation ◻ is defined as follows:

Which one of the following is equivalence to $$P \vee Q$$?

For the compositive table of a cyclic group shown below

Which one of the following choices is correct?