Determine whether each set $\left\{ p_{1},p_{2} \right\}$ is a linearly independent set in ${\mathbb P}_{3}$. Type "yes" or "no" for each answer.

The polynomials $p_{1}(t)=1+t^2$ and $p_{2}(t)=1-t^2$.

The polynomials $p_{1}(t)=2t+t^2$ and $p_{2}(t)=1+t$.

The polynomials $p_{1}(t)=2t-4t^2$ and $p_{2}(t)=6t^2-3t$.