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Explanation:
We're given the following
[tex]C = \{ x | x \in \mathbb{N}, \ 30 < x < 56, \ \text{ x is divisible by 6}\}[/tex]
which means that we have a set of natural numbers between 30 and 56, excluding both endpoints, and the set of numbers are also multiples of 6.
So looking at the multiples of 6 that are between 30 and 56 leads us to
{30, 36, 42, 48, 54}
but we cross off 30 as we want x to be larger than that, so we get this updated final list
{36, 42, 48, 54}
There are four items in this final list so the cardinality of the set described is 4. The cardinality is just the number of items in a given set.
