[(p → q) ∧ (q → r)] → (p → r)
(p → q)=P'+Q== region(2,3,6,8)+region (2,4,6,7)=region (2,3,4,6,7,8) .. (Here + is equivalent to logical OR)
Q->R =Q'+R== region(1,3,5,6,7,8)
P->R=P'+R== region(2,3,5,6,7,8)
[(p → q) ∧ (q → r)] == Region (3,6,7,8) .....1
(p → r) ........2
[(p → q) ∧ (q → r)] → (p → r) == 1->2== 1'+2 == Region(1,2,4,5)+Region(2,3,5,6,7,8)=Region (1,2,3,4,5,6,7,8) Hence Tautology