What about the cardinality of Cartesian products? So if we have sets:
\(\{1,2,3\}\)
\(\{a,b\}\)
We can have the Cartesian product set:
\(\{(1,a),(2,a),(3,a),(1,b),(2,b),(3,b)\}\)
We can see that:
\(|A.B|=|A|.|B|\)
\(|A\lor B| = |A|+|B|-|A\land B|\)
\(|P(s)|=2^{|s|}\)
\(|a \setminus b|=|a|-|a\land b|\)
What about the cardinality of even numbers? Well, we can define a bijective function between each:
\(f(n)=2n\)
Similarly for odd numbers:
\(f(n)=2n+1\)
So these both have cardinality \(\aleph_0\).