Question

Let B be a standard deck of 52 playing cards. Each card is in one of four suits ⋄,⋄,⋄, and ⋆. The names of the suits in order are Spades, Hearts, Diamonds and Clubs. Each card also has a rank from the set A,1,2,3,4,5,6,7,8,9,10,J,Q,K where A is for Ace, J is for Jack, Q is for Queen and K is for King.

a) Define an equivalence relation E on B by xEy if and only if x and y have the same rank. List the cards that are equivalent in E to the Queen of Diamonds.

b) Define an equivalence relation F on B by xFy if and only if x and y have the same suit. List the cards that are equivalent in F to the Queen of Diamonds.

Answer 1

For the equivalence relation E, the Queen of Diamonds is equivalent to the Queen of Clubs, Hearts, and Spades. For the equivalence relation F, the Queen of Diamonds is equivalent to all other Diamonds cards.

Step-by-step explanation:

a) To define an equivalence relation E on B, we say that xEy if and only if x and y have the same rank. So, in this case, the Queen of Diamonds would be equivalent to the Queen of Clubs, the Queen of Hearts, and the Queen of Spades. These are the cards that have the same rank as the Queen of Diamonds.

b) To define an equivalence relation F on B, we say that xFy if and only if x and y have the same suit. So, in this case, the Queen of Diamonds would be equivalent to all of the other cards in the Diamonds suit. These are the cards that have the same suit as the Queen of Diamonds.