##### Gate-2015 Power set

Example:1

If the power set of A is denoted as P(A) and   Which of the following options are true?

A.

B.

C.

D.

1. A and C only
2. B and C only
3. A , B and C only
4. A, B and D only

Solutions:-

P(A) = { ϕ ,  {5} ,   {{6}}    ,  {{7}}  ,  {5, {6}}  ,  {5, {7}}   ,  { {6} , {7} } , {5, {6} , {7}} }

Clearly  and   But

means the elements { 5, {6}} belongs  to P(A)

means the elements  { 5, {6}}  is subest of P(A)  which is wrong . Think why??

Because an element of a set can't be the subset of a set.  Instead of { 5, {6}}  if { { 5, {6}} } was given then that could be correct.

Example:

A={1,2,3}

1 can't be a subset of A but {1} is a subset of A. Before a  set s' become a subset of some set S, s' should be a set first.

So only A, B, C are correct.