Let us prove that

((pq) (rq)) (pr)

Is a logical law, i.e. it is always true.

We will assume that ((pq) (rq)) (pr)

can be false, and show that our assumption leads to a Contradiction

Please insert truth values (1 or 0 after =) below

1. Assume ((pq) (rq)) (pr)=0
2. (pq) (rq)= [1]
3. pr= [1]
4. p= [3]
5. r= [3]
6. pq= [2]
7. rq= [2]
8. q= [6, 4]
9. q= [8]
10. r= [5]
11. q= [7,10]

Do you see a Contradiction?