Page 17 - Mathematics Class - XI

Viva-Voce

1. Is A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)? How can we verify this property?
Ans. Yes, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). It is the other distributive law. This property can also be verified
like the above activity.
2. If A = {1, 2, 3}, B = {3, 4} and C = {3, 5, 7}, verify A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
Ans. (B ∩ C) = {3}

Then, A ∪ (B ∩ C) = {1, 2, 3}
A ∪ B = {1, 2, 3, 4}
A ∪ C = {1, 2, 3, 5, 7}
Then, (A ∪ B) ∩ (A ∪ C) = {1, 2, 3}

Hence, A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
3. What is meant by a non-empty set?
Ans. A set which has at least one element is called a non-empty set.
4. Given that {x : x ∈ W and x + 5 = 5}. Is this an empty set?

Ans. No, this is not an empty set because
{x : x ∈ W and x + 5 = 5} = {0}, which is a non-empty set.
5. What is the complement of universal set?
Ans. Null set or φ

6. What are the distributive laws of algebra of set?
Ans. (i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
(ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

MCQs

1. (A ∪ B ∪ C)' equals to
a) A ∩ B ∩ C b) A' ∩ B' ∩ C' c) A ∪ B ∪ C d) None of these
2. A survey shows that 63% people see a news channel while 76% people see an other channel. If x% people
see both channels then

a) x = 35 b) x = 63 c) 39 < x < 63 d) x = 39
3. If n(A) = 20, n(A ∪ B) = 42 and n(A ∩ B) = 4 then the value of n (A – B) is

a) 16 b) 25 c) 30 d) None of these
4. The value of A ∩ A' is equal to
a) A' b) A c) φ d) A ∪ B

Answers: 1. b) A' ∩ B' ∩ C' 2. c) 39 < x < 63 3. a) 16 4. c) φ

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