Another way to do this is to construct a "truth table". p, q, and r can each be "T" or "F" so there are cases.
If p= q= r= T, then is true and is true so is true. Also then [tex]q\wedge r[/itex] is true so is true. Since they are both true in this case.
If p= F, which includes 4 of the 8 cases, each of , , and is true because " " is true no matter what x is.
Now show they are the same in the other 3 cases.