If p, q and r are simple propositions such that (p∧q)∧(q∧r) is true, then
p, q and r are all false
p, q and r are all true
p, q are true and r is false
p is true and q, r are false
(p∧q)∧(q∧r) is true which means that p∧q and q∧r are both true.
Therefore, p, q and r are all true.