Question

4. Casino Slim, world-renowned riverboat gambler, reasons as follows Sneaky Sally's hand is a flush. Every full house beats Sneaky Sally's hand. Sneaky Sally's hand beats any pair. The relation of one hand beating another is transitive. Thus any full house beats any pair. Use the following symbolization key to symbolize Casino Slim's reasoning. (5 points for each sentence and 5 points for identifying the premises and the conclusion; 30 points total) Poker hands x is a full house x is a flush x is a pair Bxy: x beats y Sneaky Sally's hand UD: Hx: Fx: Px: S:

hi please show all work thanks

Answer 1

The premises are:

1. Fs ("Sneaky Sally's hand is a flush")

2. ∀x(Hx → Bxs) ("Every full house beats Sneaky Sally's hand" is equivalent to

"if x is a full house then x beats s")

3. ∀y(Py → Bsy)  ("Sneaky Sally's hand beats any pair ")

4.  ∀x, ∀y, ∀z ((Bxy^ Byz) → Bxz) ("The relation of one hand beating another is transitive ")

The conclusion is

5. ∀x, ∀y ((Hx^ Py) → Bxy) ("Any full house beats any pair)