Let f$,$ g in I$($X$,\backslash$Sigma $,)$ be such that f $+$ g$,\backslash$alpha f in I$($X$,\backslash$Sigma $,)$ for $\backslash$alpha in R$.$ Prove that ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}($f $+$ g$)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$f $+{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$g and ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\backslash$alpha f$)=\backslash$alpha ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$f