# Idea of a Set

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• Q1

The set {x : x is an even prime number} can be written as

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{2}

##### Explanation:

Note that 2 is the only even prime number.

So, the required set is {2}.

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• 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: x2 = 16, x N}

(iv) {x : |x| < –2, x N}

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##### Answer:

(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.

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• Q3

If A, B, C be three sets such the A B = A C and A B = A C, then

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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

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• 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 are

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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.
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• Q5

A set A has 3 elements and another set B has 6 elements. Then

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6 n (AB)9

##### Explanation:
We have

Min n (AB) = max {n(A), n (B)} = max {3, 6} = 6

Max n (AB) = n (A) + n (B) = 9

6n (AB)9

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