Question

Problem 4 [25 pts]: Playing Cards Let C represent a set of 52 playing cards with four suits(♡₂each having 13 ranks (Ace,2,3,4,5,6,7,8,9,10,Jack, Queen, King). The 's and 's arered cards. The's and's are black. We define the following additional sets. F=Face cards(Jack, Queen, and King). R=Red cards. P=Cards having a rank that is a prime number (2,3,5,7).J =One-eyed Jacks (Jack of Hearts, Jack of Spades). 1. Depict these sets as a Venn Diagram and show the cardinality of each distinct region. The regions don't have to be perfectly to scale - this can be hand-drawn. Only overlap sets that truly overlap. Disjoint sets, those sharing no members, should be rendered as non-overlapping. 2. Using set notation, give an expression for the set of cards that are red or face cards or prime numbered or one-eyed Jacks and compute its cardinality. 3. Give a set expression and compute the cardinality for the set of cards that are not face cards or not prime-numbered cards. 4. Give a set expression and compute the cardinality for the complement of the set of cards that are red or prime-numbered but not one-eyed Jacks. 5. Give a set expression and compute the cardinality for the set of cards that are either red non-prime cards or one-eyed Jacks, but not both.

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