Sets

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  • Q1

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

    Marks:1
    Answer:

    {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}

    Marks:1
    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

    Marks:1
    Answer:

    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

    Marks:1
    Answer:

    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

    Marks:1
    Answer:

    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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