Set theory!

Probability Level 1

Let $A$ and $B$ be two sets and $U$ be a universal set such that $|U|=700$ , $|A|=200$ , $|B|=300$ and $|A\cap B|=100$ . Find $|A^{C}\cap B^{C}|$ .

100 200 400 300

1 solution

Zandra Vinegar Staff
Oct 12, 2015

The elements that either aren't in A and that aren't in B are those that aren't in A or B $= (A \cup B)^C$

$|A \cup B| = |A| + |B| - |A \cup B| = 200 + 300 - 100 = 400$ $|A \cup B|^C = |U| - |A \cup B| = 700 - 400 = 300$

Shouldn't the cardinality of A union B be equal to the cardinality of A plus the cardinality of B minus the cardinality of A intersect B (not union )?

Chris Leonard - 3 years ago

Yeah I'm guessing that was a typo.

Tristan Goodman - 11 months, 2 weeks ago

Set theory!

1 solution

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