The Boolean Expression (p∧¬q)∨q∨(¬p∧q) is equivalent to:

(p∧¬q)∨q∨(¬p∧q)
This is equivalent to=
(p∨q)∧(¬q∨q)∨(¬p∧q)=
[(p∨q)∧t]∨(¬p∧q)=
(p∨q)∨(¬p∧q)=
(p∨q∨¬p)∧(p∨q∨q)=
(t∨q)∧(p∨q)=
(t∧(p∨q))=
p∨q