Determine whether each of the following is true or false. In each case, assume \(P\) is located at \(t=0\) and \(F\) is located at \(t=n\), and the \(A\) s are spread uniformly over the planning horizon.

a. \((A \mid P i \%, 1)=(F \mid P i \%, 1)\)

b. \((A \mid P i \%, n)=(F \mid P i \%, n)\); for \(n>1\)

c. \(P(A \mid P i \%, n)=P(F \mid P i \%, n)(A \mid F i \%, n)\)

d. \(F(A \mid F i \%, n)=F(P \mid F i \%, n)(A \mid P i \%, n)\)

e. \(P(A \mid P i \%, n)=P(A \mid P i \%, n-3)+P(A \mid P i \%, 3)\); for \(n>3\)

f. \(P(A \mid P i \%, n)=P(A \mid P i \%, n-3)(A \mid P i \%, 3)\); for \(n>3\)