how do I go about finding set sizes?
Example
|A| = 129; |B| = 53; |A ∩ B| = 34; |A ∪ B| =
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2Drawing a Venn diagram is very useful here. – Olivier Moschetta Sep 21 '20 at 20:44
2 Answers
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Well, the additive rule (probably) says
$$|A \cup B| = |A| + |B| - |A \cap B|$$
which should be all the info you need.
Henno Brandsma
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Amount of elements that are in A is 129
Amount of elements that are in B is 53
Amount of elements that are in A and in B at the same time is 34
So
Amount of elements that are only in A is 129-53=95
Amount of elements that are only in B is 53-34=19
Amount of elements that are in A or in B is equal to amount of elements that are only in A + amount of elements that are only in B + amount of elements that are in both A and B at the same time = 95 + 19 + 34 = 148
That's why $$|A\cup B|=148$$
Alternative approach
Size of the set $A\cup B $ is equivalent to sum of sizes of $A$ and $B$ with size of $|A\cap B|$ substracted.(if you think about it, it seems obvious)
Amad
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