Determine whether each set $\{p_1,p_2\}$ is a linearly independent set in $P_3.$ 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 $p_2(t)=6t^2-3t.$