Question

Let A={n∈N:20≤n<50} and B={n∈N:10<n≤30}. Suppose C is a set such that C⊆A and C⊆B. What is the

largest possible cardinality of C?

Answer 1

Let $A=\{n∈\N:20≤n<50\}$ and $B=\{n∈\N:10<n≤30\}$. Suppose $C$ is a set such that $C⊆A$ and $C⊆B.$

The largest set that is contained in $A$ and $B$ is $A\cap B.$ Taking into account that the cardinality of $A\cap B=\{20,21,22,23,24,25,26,27,28,29,30\}$ is equal to 11, we conclude that the largest possible cardinality of $C$ is 11.