# The Dayenu Boolean Function Is Almost Always True!

## TL;DR

This paper analyzes the Dayenu Boolean function, showing that for n miracles, the number of satisfying truth assignments is 2^n minus (n+1), revealing its near-universal truthfulness.

## Contribution

It formally expresses the Dayenu function in conjunctive normal form and derives an exact count of its satisfying truth vectors.

## Key findings

- Number of satisfying truth-vectors is 2^n - (n+1)
- The function is almost always true for large n
- Provides a formal logical analysis of a cultural song

## Abstract

The Boolean function implicit in the famous Dayenu song, sung at the Passover meal, is expressed in full conjunctive normal form, and it is proved that if there are n miracles the number of truth-vectors satisfying it is $2^n -(n+1)$.