Question

Find cardinality of set B

B = {∅, {1}, {1, 2}, {1, 2,3}, · · · , {1, 2, · · · , m}}

Answer 1

The cardinality of set B is m + 1

Explanation:

Here, the given set,

B = {∅, {1}, {1, 2}, {1, 2,3}, · · · , {1, 2, · · · , m}},

Since, the elements of S are,

∅ , {1}, {1, 2}, {1, 2, 3}....... {1, 2,.....m }

By observing the set,

We found that, every next set contains one more succeeding natural number than the previous set.

So, if the last set contains m natural numbers.

Then there are 'm + 1' sets in B ( m sets included ∅ )

Hence, the number of elements in B is 'm+1'

Now, cardinality of a set is the number of elements contained by the set.

I.e. the cardinality of set B is m + 1.