Fill in the blanks to make each of the following a true statement :
(i) A ∪ A′ = . . .   (ii) φ′ ∩ A = . . .
(iii) A ∩ A′ = . . . (iv) U′ ∩ A = . . .

Solution:

We will fill in the blanks to make each of the following a true statement.

Let us assume that U is the universal set.

We know that the complement of a set A is denoted by A′ and A′ contains all the elements of U that are NOT in A.

Then

(i) A υ A' = U

(ii) Φ' ∩ A = U ∩ A = A

(iii) A ∩ A' = Φ

(iv) U' ∩ A = Φ ∩ A = Φ

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.5 Question 7

Fill in the blanks to make each of the following a true statement : (i) A ∪ A′ = . . . (ii) φ′ ∩ A = . . . (iii) A ∩ A′ = . . . (iv) U′ ∩ A = . . .

Summary:

We are asked to fill in the blanks to make each of the following a true statement. We have found that A υ A' = U, Φ' ∩ A = A, A ∩ A' = Φ and U' ∩ A = Φ.