If (P → q) → (q → r) is false then (p → q) must be true and (q → r) must be false. Now, If P → q is true then P & q both can be true or false : If q → r is false then q must be true and r must be false So when both condition i.e. P → q true and q → r false satisfy then q is true, r is false and P can be true or false