Normality is not hereditary

This article gives the statement, and possibly proof, of a topological space property (i.e., normal space) not satisfying a topological space metaproperty (i.e., subspace-hereditary property of topological spaces).
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This article gives the statement and possibly, proof, of a non-implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Normal space (?)) need not satisfy the second topological space property (i.e., Hereditarily normal space (?))
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Statement

It is possible to have a normal space $X$ and a subset $A$ of $X$ such that $A$ is not a normal space in the subspace topology.

In other words, it is possible to have a normal space that is not a hereditarily normal space.