Your problem is missing parentheses, and is ambiguously written. As it stands, it may be true or false. But whatever it is, you can prove it with a truth table or by casework.
If we read it as (p∧¬q)∨(q∧¬r)∨(¬p∨r), then it is true. The rightmost disjunct renders the statement true if either r is true or p is false. But if we assume r is false and p is true, we get (T∧¬q)∨(q∧T)∨F, which is equivalent to q∨¬q since (A∧T) is equivalent to A and (B∨F) is equivalent to B.
If we read it as ((((p∧¬q)∨q)∧¬r)∨¬p)∨r, the sentence is conditional. Let p and q be false, and evaluating left-to-right gets us
((((F∧T)∨F)∧¬r)∨T)∨r ≡ (((F∨F)∧¬r)∨T)∨r ≡ ((F∧¬r)∨T)∨r ≡ (F∨T)∨r ≡ T∨r ≡ r
