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.
