26.7k views
3 votes
Ifn(r'ns')+ n(r'ns)=3 n(r n s) = 4 & n(s'nr)= 7 find n(u).

1 Answer

3 votes

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

__

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

User Nicholas Palko
by
8.0k points