Argue that $$logically implies$$ has the following property $($called transitivity$)$ on

the set of all statements: if a$,$ b and c are statements such that a $$ b and b $$ c$,$

then a $$ c$.$

$($b$)$ Suppose a$,$ b$,$ c and d are statements such that a $$ b$,$ b $$ c$,$ c $$ d$,$ and d $$ a$.$

Argue that any two of these statements are logically equivalent. $($Hint: part $($a$).)$