Double double Role.

Probability Level 2

$\color{maroon}{A=\{ \{ \} \}}$

Find the cardinal number of the set $\color{maroon}{A}$ .

Note : Cardinal number of a set is equal to the number of elements contained in the set.

Join the Brilliant Classes and enjoy the excellence. Also checkout Foundation Assignment #2 for JEE.

0 2 1 None of the given choices. can't be predicted.

1 solution

Rahul Singh
May 29, 2015

The set 'A' is effectively equivalent to the NULL SET because the inner set is also a NULL SET & can simply be removed to simplify the solution.

Now, we know that the NULL SET contains a single element 'phi' , Hence the solution is 1.

Rahul Singh Your solution is not correct.

Null set contains no element. But you're saying through your solution that null set contains a single element 'phi'.

The fact is that 'phi' is just a symbol to denote the null set. ie. $\phi=\{ \ \}$

But here in this question the inner null set is an element of the set $A$ . So we can say that set $A$ equivalent to $\{ \phi \}$ . So $A$ contains one element as $\{\phi\}$ .That's why the answer is given $1$ .

Sandeep Bhardwaj - 6 years ago

If I'm not wrong, the given set A is the power set of any null set

Dinesh Nath Goswami - 6 years ago

You're absolutely right ! Great observation ! Keep it up.

Sandeep Bhardwaj - 6 years ago

Oops!! Inadequate information of mine...thanks for correcting me sir...appreciate that...

Rahul Singh - 6 years ago

Double double Role.

Join the Brilliant Classes and enjoy the excellence. Also checkout Foundation Assignment #2 for JEE.

1 solution

0 pending reports