Confusion in answering question related to the inclusion-exclusion principle

[user4792]

Source: Gregmat - Tickbox Quix 14
Answer Key = D
My answer: A

I used the formula for inclusion-exclusion principle from the quant mountain:
Total = A + B - Both + None
100 = 80 + 40 - Both + None
Both = 120 - 100 + None
Both = 20 + None

The way I understand the question is that ‘None’ (i.e. households with no sons and daughters) cannot be zero bcs it’s explicitly stated that “every family has a son, a daughter, both, or none”. As such, shouldn’t the ‘Both’ be >20?

[Leaderboard]

@user4792

‘None’ (i.e. households with no sons and daughters) cannot be zero

Just because something does not have to be zero does not mean that it cannot be zero.