Ten > Sets
In sets A and B, A has 50 members, B has 60 members, and 30 members are the same in both sets. By how many elements $\rm (A \cup B)$ is formed?
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Atith Adhikari
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2 years ago
Solution
Let the cardinality of sets A and B be represented by n(A) and n(B), respectively.
According to the question,
$\rm n(A) = 50, n(B) = 60, n(A \cap B) = 30$
To find: $\rm n(A \cup B) = ?$
We use the formula for the union of two sets to find the cardinality of the intersection of those sets, we get,
$\rm n(A \cup B) = n(A) + n(B) - n(A \cap B)$
$\rm or, n(A \cup B) = 50 + 60 - 30$
$\rm n(A \cup B) = 110 - 30$
$\rm \therefore n(A \cup B) = 80$
Hence, 80 members form the set $\rm n(A \cup B)$.
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