[Verse 1]
When counting scattered puzzle pieces across the floor
Some land in boxes, some spill through the door
If sets collide like planets in space
We can't just add them face to face
The overlap creates a sneaky trap
Elements counted twice upon our map
So mathematics gives us one neat trick
The inclusion-exclusion arithmetic
[Chorus]
Add them up, subtract what's shared
Triple meetings must be repaired
Back and forth the signs will dance
Plus and minus in perfect balance
Union size through alternating eyes
Every element counted once, no lies
[Verse 2]
For two circles meeting on a page
Simple formula takes center stage
A plus B minus where they cross
Prevents the double-counting loss
But three sets weave a complex web
Individual counts where we must tread
Minus pairs that intersect in two
Plus the center where all three break through
[Chorus]
Add them up, subtract what's shared
Triple meetings must be repaired
Back and forth the signs will dance
Plus and minus in perfect balance
Union size through alternating eyes
Every element counted once, no lies
[Bridge]
First we overcount with reckless glee
Then subtract to fix what we can see
But now we've gone too far the other way
Add back what we stole in our display
The pattern grows with each new set we bring
Alternating signs like bells that ring
N plus one determines if we add or take
A mathematical rhythm we cannot break
[Chorus]
Add them up, subtract what's shared
Triple meetings must be repaired
Back and forth the signs will dance
Plus and minus in perfect balance
Union size through alternating eyes
Every element counted once, no lies
[Outro]
When sets unite in endless ways
The principle forever stays
Through zigzag signs we find our truth
Inclusion-exclusion, mathematical proof