$(3$ MARKS$)$ Prove by induction $($on length of formula construction or on

complexity$)$ or directly via the recursive definition of wff that no wff is

the empty string.

$(2$ MARKS$)$ Prove by induction $($on length of formula construction or on

complexity$)$ or directly via the recursive definition of wff that every for$-$

mula has as rightmost symbol either a right bracket or an atomic formula.