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Probability Level 2

$A =\{\phi, \{\phi\}, \{\phi\, \{\phi\}\}\}$

How many subsets does $A$ have?

8 4 2 0

1 solution

Ashish Menon
Apr 22, 2016

The answer 0 is a common misconception.

If $\phi$ is written inside {}, then it is considered as a non-empty set. The way of representing a null set is $\phi$ or {} and not $\{\phi\}$ .

So, the number of subsets of A = $2^{n(A)}$ = $2^3$ = $\boxed{8}$

Good problem. The challenge in this problem is to identify that set $A$ only has 3 elements. Then by rule of product , we get total number of subsets are $2^{3}= 8$ .

Pranshu Gaba - 5 years, 1 month ago

Wait, maybe

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