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Problem 4 [20 pts]: Playing Cards Let C represent a set of 52 playing cards with...

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Advance Math

Problem 4 [20 pts]: Playing Cards Let C represent a set of 52playing cards with four suits (♥, ♦, ♣, ♠) each having 13 ranks(Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King). We define the followingadditional sets. F =Face cards (Jack, Queen, and King). R =Redcards. P =Ranks that are prime (2,3,5,7). J =One-eyed Jacks (Jackof Hearts, Jack of Spades).

1. Depict these sets as a Venn Diagram and show the cardinalityof each distinct region. (The regions don’t have to be perfectly toscale - this can be hand-drawn.)

2. Using set notation, give an expression for the set of cardsthat are red or face cards or prime numbered or one-eyed Jacks andgive its cardinality.

3. Give a set expression and cardinality for the set of cardsthat are not face cards or not prime-numbered cards.

4. Give a set expression and cardinality for the complement ofthe set of cards that are either red or prime-numbered but notone-eyed Jacks.

5. Give a set expression and cardinality for the set of cardsthat are either red non-prime cards or one-eyed Jacks, but notboth.

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