For $0 \leq p \leq 1$ and for any positive $a, b$, let $I(p)=(a+b)^{p}$ and $J(p)=a^{p}+b^{p}$. Then:

• A
  $I(p) > J(p)$
• B
  $I(p) \leq J(p)$
• C
  $I(p) < J(p)$ in $[0, p/2]$ and $I(p) > J(p)$ in $[p/2, \infty)$
• D
  $I(p) < J(p)$ in $[p/2, \infty)$ and $J(p) < I(p)$ in $[0, p/2]$