To answer this question we will use the following property of sets:
[tex]|A\cup B|=|A|+|B|-|A\cap B|[/tex]
(a) Since Ash has 153 cards in his collection (without any duplicates), Brock has 207 cards in his collection (also without any duplicates) and they have 91 cards in common, then:
[tex]\begin{gathered} |AshCards\cup BrockCards|=|AshCards|+|BrockCards|-|AshCards\cap BrockCards| \\ =153+207-91. \end{gathered}[/tex]
Simplifying the above result we get:
[tex]|AshCards\cup BrockCards|=269.[/tex]
(b) Expressing the above result using set notations:
[tex]|A\cup B|=269.[/tex]
Answer:
(a) There are 269 unique cards in between them.
(b)
[tex]|A\cup B|=269.[/tex]
