Page 11 - mathsvol1ch1to3ans

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Answer: T is an equivalence relation but S is not an equivalence relation.
0 0
6. Let A and B be subsets of the universal set N, the set of natural numbers. Then A ∪[(A∩B)∪B ]
is
0
(a) A (b) A (c) B (d) N
Answer: (d) N
0 0 0 0
(A ∩ B) ∪ B = (A ∪ B ) ∩ (B ∪ B ) = (A ∪ B ) ∪ N = N
0
A ∪ [N] = N
7. The number of students who take both the subjects Mathematics and Chemistry is 70. This
represents 10% of the enrolment in Mathematics and 14% of the enrolment in Chemistry. How
many students take at least one of these two subjects?
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(a) 1120 (b) 1130 (c) 1100 (d) insufficient data
Answer:
100
Enrolment in Mathematics = % of 70% = 700
10
100
Enrolment in Chemistry = % of 70% = 500
14
Enrolment in atleast one of these two subjects = 1200 − 70 = 1130
8. If .(A × B) ∩ (A × C)] = 8 and n(B ∩ C) = 2 , then n(A) is

(a) 6 (b) 4 (c) 8 (d) 16
Answer: (A × B) ∩ (A × C) = A × (B ∩ C).
n(A × (B ∩ C) = n(A) × n(B ∩ C) = 8
Since n(B ∩ C) = 2, n(A) = 4
9. If n(A) = 2 and n(B ∪ C) = 3, then n[(A × B) ∪ (A × C)] is

(a) 2 3 (b) 3 2 (c) 6 (d) 5
Answer: (c) 6
[(A × B) ∪ (A × C)] = A × (B ∪ C)
n[A × (B ∪ C)] = n(A) × n(B ∪ C) = 2 × 3 = 6
10. If two sets A and B have 17 elements in common, then the number of elements common to the
set A × B and B × A is
(a) 2 17 (b) 17 2 (c) 34 (d) insufficient data

Answer:(b) 17 2
11. For non–empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) equal

a) A ∩ B (b) A × A (c) B × B (d) none of these.
Answer: (b) A × A
Explanation: Let (x, y) ∈ (A × B) ∩ (B × A).
(x, y) ∈ (A × B) ⇔ x ∈ A, y ∈ B
(x, y) ∈ (B × A) ⇔ x ∈ B, y ∈ A
A ⊂ B ⇔ A ∩ B = A
x ∈ A, x ∈ B ⇔ x ∈ (A ∩ B), x ∈ A
y ∈ A, y ∈ B ⇔ y ∈ (A ∩ B), y ∈ A
(x, y) ∈ A × A
(A × B) ∩ (B × A) = A × A
12. The number of relations on a set containing 3 elements is

(a) 9 (b) 81 (c) 512 (d) 1024
Answer:The number of relations = 2 3 2 = 512.
13. Let R be the universal relation on a set X with more than one element. Then R is