For $x \in \mathbb{R}$, define $\langle x\rangle=x-[x]$. Then for any arbitrary pair of real numbers $x, y \in \mathbb{R}^{+}$,

• Correct answer
  A

  $\langle x+y\rangle \leq\langle x\rangle+\langle y\rangle$
• B

  $\langle x+y\rangle \geq\langle x\rangle+\langle y\rangle$
• C

  $\langle x+y\rangle=\langle x\rangle+\langle y\rangle$
• D

  $\langle x+y\rangle \neq\langle x\rangle+\langle y\rangle$

Hence, the correct answer is option: 'A'.