Draw appropriate Venn diagram for each of the following:

(i) (A ∪ B)’, (ii) A’ ∩ B’, (iii) (A ∩ B)’ (iv) A’ ∪ B’

(i) (A ∪ B)’

First we draw (A ⋃ B)

The shaded region represents (A ⋃ B).

We have to draw diagram for complement of (A ⋃ B) i.e.(A ∪ B)’, which is given by U - (A ⋃ B).

Green region is (A ∪ B)’.

(ii) A’ ∩ B’

Here we have to draw diagram of (A’ ⋂ B’)

So, first we draw A’( = U - A)

Now, we draw B’( = U - B)

Now the area common in both the shaded regions gives us (A’ ⋂ B’)

Here, we observe that the final result for (i) and (ii) is same.

⇒ (A ⋃ B)’ = (A’ ⋂ B’)

(iii) (A ∩ B)’

First we draw (A ⋂ B)

The shaded region represents (A ⋂ B).

We have to draw diagram for complement of (A ⋂ B) i.e.(A ∩ B)’ , which is given by U - (A ⋂ B)

(iv) A’ ∪ B’


Here we have to draw diagram of (A’ ⋃ B’)

So, first we draw A’( = U - A)

Now, we draw B’( = U - B)

Now the area present in both is added to give (A’ ⋃ B’)

Here, we observe that the final result for (iii) and (iv) is same.

⇒ (A ⋂ B)’ = (A’ ⋃ B’)