(i) (A ∪ B) ∩ C
Firstly we shade the area of A and B by horizontal lines which represent A ∪ B. Then we shade the area of (A ∪ B) ∪ C by vertical lines.
The cross shaded area represents the area of (A ∪ B) ∩ C.
(ii) (A ∩ B) ∩ C
Firstly we shade the common area of A and B which represent (A ∩ B) after that we shade the area of (A ∩ B) and C which represent (A ∩ B) ∪ C.
(iii) A’ ∪ B’
A’ = U – A, B’ = U – B
Horizontal shaded region A’ vertical shaded region B’
Hence, whole shaded region = A’ ∪ B’
(iv) (A ∪ B)’
The shaded region is (A ∪ B)’
Hence Proved.
