Set has more elements than set . The two sets have elements in common, and the total number of unique elements across both sets is
How many elements set have?
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∣ A ∪ B ∣ = ∣ A ∣ + ∣ B ∣ − ∣ A ∩ B ∣ .
Since A consists of 1 0 more elements than set B , then ∣ B ∣ = ∣ A ∣ − 1 0 .
Since 7 elements are in common to both A and B , then ∣ A ∩ B ∣ = 7 .
Since A and B have 8 5 unique elements ⟹ ∣ A ∪ B ∣ = 8 5 .
∣ A ∪ B ∣ = ∣ A ∣ + ∣ B ∣ − ∣ A ∩ B ∣
8 5 = ∣ A ∣ + ∣ A ∣ − 1 0 − 7 ⟹ 1 0 2 = 2 ∣ A ∣ ⟹ ∣ A ∣ = 5 1 .
Set A has 5 1 elements.
Note: ∣ S ∣ = number of elements in a set S .