Please help with indetifying subformulas in the propositional logic. In my textbook of the propositional logic I should indentify all subformulas of the following formula: ¬(a∧b)⟺(c⇒a).
According to the textbook the formula (a∧b)⟺(c⇒a) is not a subformula of the formula ¬(a∧b)⟺(c⇒a). Why?
They also argue that ¬(a∧b)⟺(c⇒a) is a subformula of itself, is that correct?

If the statement was ¬[(a∧b)⟺(c⇒a)] (i.e. if the statement was the negation of a biconditional), then (a∧b)⟺(c⇒a) would indeed be a subformula. But, the given formula ¬(a∧b)⟺(c⇒a) is a biconditional between ¬(a∧b) and c⇒a. So, those are both subformulas, but (a∧b)⟺(c⇒a) is not
Keep in mind that a subformula is not the same as a substring! Rather, try and understand how the operations are applied to the parts: that will tell you waht the subformulas are.
And yes, any formula is a subformula of itself ... kind of like how every set is a subset of itself.  If we want to exclude the formula itself, we would call for strict subformulas.
