Intuitionistic logic unit type as truth

Question

I am trying to learn constructive logic. Why can true be represent as a unit type while false is represented as the void type?

Answer 1

The main reason is categorical. If you see logic through the category-theoretic lens, true is the terminal object, and false the initial object. In $Set$, the category whose objects are sets and arrows are maps, the initial object is the empty set, and the singleton is the terminal object.

In a simpler way, it relates to the notion of inhabited type (set) in constructive mathematics, where if a type is consistent you can construct a witness, while you can't build a proof of false (so false is empty).