$($a$)$ Let $F_k=F_{k-1}+F_{k-2}$ with $F_1=1$ and $F_2=1.$ Prove by induction that $F_{m+1}*F_{m-1}-F_m^2=(-1{)}^m.$

$($b$)$ Prove by contradiction that pvvnotp$=$ True for every proposition $p.$

$($Recall that a proposition is a statement that is true or false. That is$,$ we have either $p=$ True or $p=$ False for a given

proposition $p.$ We assume that you know logical or $(vv)$ and negation $(not)$ operators. If not please refer to your discrete

math textbook or search on internet.$)$