(1) Write down the power set  of  A  =  { 10, 20, 30 }.

Soln. P (A)  =  {  , {10}, {20}, {30}, {10, 20}, {10, 30}, {20, 30}, {10, 20, 30} }

(2) Write down the power set of  A  =  { a, { b, c } }.

Soln. We have :  A  =  { a, B },  where  B  =  { b, c }.

P (A)  =  {   , {a}, {B}, {a, B} }

=   {   , {a}, {{b, c}}, {a, {b, c}} }.

(3) A survey shows that 78% of  the Indians like apples whereas  68% like oranges. What percentage of  Indians like both apples and oranges ?

Soln. A  :  Indians like apples   &   O  :  Indians like oranges

n ( A  O )  =  n ( A ) + n ( O ) – n ( A  O )

  100  =  78  +  68  – n ( A  O )

  n ( A  O )  =  146  –  100

  n ( A  O )  =   46

(4) In  a group of  1000 persons, 780 can speak Hindi and  450 can speak Bengali. Find : (i)  how many can speak both Hindi and Bengali;

           (ii)  how many can speak Hindi only;

          (iii)  how many can speak Bengali only.

Soln. H  :  Persons speak Hindi   &

B  :  Persons speak Bengali

  n ( H  B )  =  n ( H ) + n ( B ) – n ( H  B )

1000  =  780  +  450  – n ( H  B )

n ( H  B )  =  1230  –  1000

n ( H  B )  =   230

Ans  :  (i)  =  230,    (ii) = 550    &    (iii)  =  220

(5) If  A  =  { a, b },  B  =  { a, c, e }, then find :

(i)  A  B          (ii)  B A       (iii)              (iv)   

Soln. (i) A  B  =  { a, b } { a, c, e }  =   { (a, a), (a, c), (a, e), (b, a), (b, c), (b, e) }

 (ii) B  A  = { a, c, e }  { a, b }   =  { (a, a), (a, b), (c, a), (c, b), (e, a), (e, b) }

(iii)  =  A A  =  { a, b } { a, b } =  { (a, a), (a, b), (b, a), (b, b) }.

(iii)  =  B  B  =  { a, c, e } { a, c, e }=  { (a, a), (a, c), (a, e), (c, a), (c, c), (c, e), (e, a), (e, c), (e, e) }.