A Binary operation $$ \oplus $$ on a set of integers is defined as $$x$$ $$ \oplus $$ $$y$$ $$ = {x^2} + {y^2}$$. Which one of the following statements is TRUE about $$ \oplus $$ ?

Consider the set $$S = \left\{ {1,\,\omega ,\,{\omega ^2}} \right\},$$ where $$\omega $$ and $${{\omega ^2}}$$, are cube roots of unity. If $$ * $$ denotes the multiplication operation, the structure $$\left\{ {S,\, * } \right\}$$ forms

What is the possible number of reflexive relations on a set $$5$$ elements?

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?