Idea of a Set
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Q1
The set {x : x is an even prime number} can be written as
Marks:1Answer:
{2}
Explanation:
Note that 2 is the only even prime number.
So, the required set is {2}.

Q2
Which of the following sets are null sets?
(i) The set of all prime numbers lying between 15 and 19(ii) {x : x < 5 and x > 6}
(iii) {x: x^{2} = 16, x N}
(iv) {x : x < –2, x N}
Marks:1Answer:
(ii) and (iv).
Explanation:
As there is no such number which is greater than 6 as well as less than 5.
So {x : x < 5 and x > 6} is a null set.
Also x is always +ve so there exists no number which satisfies the condition x < –2
So {x : x < –2, x N} is also a null set.

Q3
If A, B, C be three sets such the A B = A C and A B = A C, then
Marks:1Answer:
B = C.
Explanation:
A B = A C
(A B) C = (A C) C
(A C) (B C) = C
(A B ) (B C) = C (i)
Again, A B = A C
(A B) B = (A C) B
B = (A B) (C B)
B = (A B) (B C)  (ii)
from (i) and (ii)
B = C

Q4
(I) A = {4, 6, 7, 9, 10}
(II) B = {a, b, c, 10, 9}
(III) C ={9, 3, 6, 4, 2, 1}
From the above data, equivalent sets areMarks:1Answer:
A and B.
Explanation:
Both A and B contain equal number of elements all of which are not identical. So A and B are equivalent sets. 
Q5
A set A has 3 elements and another set B has 6 elements. Then
Marks:1Answer:
6 n (AB)9
Explanation:
We haveMin n (AB) = max {n(A), n (B)} = max {3, 6} = 6
Max n (AB) = n (A) + n (B) = 9
6n (AB)9