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In: Advanced Math

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

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

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 give its cardinality.

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

4. Give a set expression and cardinality for the complement of the set of cards that are either red or prime-numbered but not one-eyed Jacks.

5. Give a set expression and cardinality for the set of cards that are either red non-prime cards or one-eyed Jacks, but not both.

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Expert Solution

Colby Messinger answered 1 year ago
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