Draw appropriate Venn diagram for each of the following:(i) (A ∪ B)′, (ii) A′ ∩ B′, (iii) (A ∩ B)′, (iv) A′ ∪ B′

Solution:

Let us draw the appropriate Venn diagram for each of the given sets.

In each of the following diagrams, the shaded region (in yellow) represents the answer.

(i) We know that (A υ B)' = U - (A υ B).

Thus, in the Venn diagram of (A υ B)',

we have to shade the entire region of U excluding A υ B.

(ii) A' ∩ B' 

By a Demorgan law of sets, A' ∩ B'  = (A ∪ B)′. Thus, its Venn diagram is as same as that of (i).

(iii) We know that (A ∩ B)' = U - (A ∩ B). Thus, in the Venn diagram of (A ∩ B)', we have to shade the entire region of U excluding A ∩ B.

(iv) A' υ B'

By a Demorgan law of sets, A' υ B'  = (A ∩ B)′. Thus, its Venn diagram is as same as that of (iii).

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.5 Question 5

Draw appropriate Venn diagram for each of the following : (i) (A ∪ B)′, (ii) A′ ∩ B′, (iii) (A ∩ B)′, (iv) A′ ∪ B′

Summary:

We are asked to draw appropriate Venn diagram for each of the following : (i) (A ∪ B)′, (ii) A′ ∩ B′, (iii) (A ∩ B)′, (iv) A′ ∪ B′. We have drawn the Venn diagrams successfully