Answer:
14
Explanation:
You want to know the size of the universal set if ...
- n(r'∩s') +n(r'∩s) = 3
- n(r∩s) = 4
- n(s'∩r) = 7
Universe
The given sets are mutually exclusive and exhaustive, so the sum of their sizes is the size of the universal set:
n(u) = 3 + 4 + 7
n(u) = 14
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Additional comment
(r'∩s') ∪ (r'∩s) = r'∩(s' ∪ s) = r' . . . . n(r') = 3
(r∩s) ∪ (r∩s') = r∩(s ∪ s') = r . . . . . . n(r) = 4 +7 = 11
Then r' ∪ r = u, the universal set. . . . . n(u) = 3 +11 = 14