For any two sets in a universal set, the number outside their union is…

Question

For any two sets in a universal set, the number outside their union is found from:

Accepted Answer

A. $n(U)-n(C\cup M)$

1. The universal set splits into two parts: what is inside the union and what is outside it.
2. So $n(U)=n(C\cup M)+n(C\cup M)'$.
3. Rearranging gives $n(C\cup M)'=n(U)-n(C\cup M)$.
4. In the farmers' problem this ran the other way: 10 outside gave a union of $50-10=40$.
5. Subtracting the intersection instead of the union double counts the members who belong to only one set.
_Source: NECTA CSEE 2022 Basic Mathematics 041, Question 3: Sets and Probability_

Answer

$n(U)+n(C\cup M)$

Answer

$n(C)+n(M)$

Answer

$n(U)-n(C\cap M)$

For any two sets in a universal set, the number outside their union is found from:

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