What are union and intersection types?

Question presented to candidate: "Explain union and intersection types. When would you reach for A | B versus A & B, and what happens to the members you are allowed to use in each case?"

What a strong answer should cover:

• A union A | B means the value is one of the types; only members common to every member are usable until you narrow (typeof, in, a tag check)
• An intersection A & B means the value is all of the types at once; it has every property of each part, which is how you compose object types
• The counter-intuitive set view: a union of object types allows more values but fewer usable properties; an intersection allows fewer values but more properties
• Incompatible intersections collapse: string & number is never, and a clash on a property makes that property (or, for literal tags, the whole object) never
• Unions are not exclusive ({ x } | { y } accepts an object with both) and & silently produces never where interface extends reports a conflict
• Practical uses: literal unions and discriminated unions for states, intersections for mixins, merge helpers and branded types

Code / implementation expected: Optional — narrow a string | number, and compose two object types with &.