For \(0 \leq p \leq 1\) and for any positive \(a, b\); let \(I(p)=(a+b)^{p}, J(p)=a^{p}+b^{p}\), then
(A) \(\mathrm{I}(\mathrm{p})>\mathrm{J}(\mathrm{p})\)
(B) \(\mathrm{I}(\mathrm{p}) \leq \mathrm{J}(\mathrm{p})\)
(C) \(I(p)<J(p)\) in \(\left[0, \frac{p}{2}\right] \& I(p)>J(p)\) in \(\left[\frac{p}{2}, \infty\right)\)
(D) \(\mathrm{I}(\mathrm{p})<\mathrm{J}(\mathrm{p})\) in \(\left[\frac{\mathrm{P}}{2}, \infty\right) \& \mathrm{~J}(\mathrm{p})<\mathrm{I}(\mathrm{p})\) in \(\left[0, \frac{\mathrm{P}}{2}\right]\)