1. Make correct statements by filling in the symbols C or ₵ in the blank spaces :-

(i) {2, 3, 4}   C          {1, 2, 3, 4, 5}

(ii) {a, b, c}             {b, c, d}

(iii) {x:x is a student of class X 1 of your School}    C   {x:x student of your school}

(iv) {x:x is a circle in the plane}    ₵    {x:x is a circle in the same plane with radius 1 unit}

(v) {x:x is a ∆ in plane}    ₵    {x:x is rectangle in plane}

(vi) {x:x is an equi. ∆ in plane}   C    {x:x is a ∆ in the plane}

(vii) {x:x is an even natural no. }   C   {x:x is an integer}.

2. Examine whether the following statements are true or false:

(i) {a, b}   ₵   {b, c, a}  False.

(ii) {a, e}   C   {x:x is a vowel in the English alphabet }     True.

(iii) {1, 3, 5}   C   {1, 3, 5}   False.

(iv) {a}   C   {a, b, c}    True.

(v) {a}   Є   {a, b, c}     False.

(vi) {x:x is an even natural no. which divides 6}   C  {x:x is a natural number which divides 36}   True.

3. Let A = {1, 2, {3, 4}, 5} which of the following statement are correct and why?

(i) {3, 4}        C          A         Incorrect.

(ii) {3, 4}       Є          A         correct.

(iii) {3, 4}      C          A         correct.

(iv) 1              Є          A         correct.

(v) 1               C         A         Incorrect.

(vi) {1, 2, 5,}            C         A         correct.

(vii) {1, 2, 3,}           Є         A         Incorrect.

(viii) {1, 2, 3,}         C         A         Incorrect.

(ix) ɸ             Є          A         Incorrect.

(x)   ɸ             C          A         correct.

(xi) {ɸ}                      C          A         Incorrect.

4. Write down all the subsets of the following subsets.

(i) {a}             =          ɸ,        {a}

(ii) {a, b}       =          ɸ,        {a}, {b}, {a, b}

(iii) {1, 2, 3} =          ɸ,        {1}, {2}, {3}, {1, 2}, {3, 1}, {2, 3}, {1, 2, 3}

(iv) ɸ             =          ɸ

How many elements has P(A) if A = ɸ?

We have,

P(A) = P(ɸ) = { ɸ}

Therefore a set containing 1 element

6. Write the following as intervals:

(i) {x:x           Є          R,        -4 < x ≤ 6}     =          (-4, 6)

(ii) {x:x          Є          R,        -12 < x < -10}          =          (-12, -10)

(iii) {x:x         Є          R,        0 ≤ x < 7}      =          (0, 7)

(iv) {x:x         Є          R,        3 ≤ x ≤ 4}      =          (3, 4)

7. Write the following intervals in set builder form:

(i) (-3, 0)       =          {x:x     Є          R,        -3 < x < 0}

(ii) (6, 12)     =          {x:x     Є          R,        6 ≤ x ≤ 12}

(iii) (6, 12)    =          {x:x     Є          R,        6 < x ≤ 12}

(iv) (-23, 5)  =          {x:x     Є          R,        -23 ≤ x < 5}

8. What universal set would you purpose for each of the following:

(i) The set of right triangles.

(ii) The set of isosceles triangles.

Sol:- Set of all triangles.

9. Given the sets A = {1, 3, 5}, B {2, 4, 6}, C = {0, 2, 4, 6, 8}, which of the following may be considered as universal sets for all the three sets of A, B and C.

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) ɸ

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set.

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11    IIT    Math    Sets    NCERT Solution Ex 3