$4.$ Consider the compound proposition X given below:

X : $$

h$($a $$ b$)->($c $$d$)$

$->$

c $$

$($a $$ b$)->$ d

i

$($a$)(4$ pt$)$ Grow a complete truth tree with root X$.$ Apply the branching rules exactly as given

in class $($don$$t use equivalences to rewrite the propositions in the tree $$ just apply the appropriate

branching rule to the proposition as written$).$ Clearly indicate which paths are active $($alive$)$

and which paths are inactive $($dead$)$ when the tree is complete

$($b$)(2$ pt$)$ Is X a contradiction? If so$,$ briefly explain the feature$($s$)$ of the truth tree that lead you

to this conclusion. If not, give all counterexamples and briefly explain the feature$($s$)$ of the truth

tree that lead you to this conclusion.