In the Rock-Scissors-Paper game, on the count of three, two players each make a

Question

In the Rock-Scissors-Paper game, on the count of three, two players each make a hand sign to represent one of the objects in the of game. The rock crushes the scissors, the scissors cut the paper, and the paper covers the rock. This defines a relation "BEATS" on the set A = {Rock, Scissors, Paper}: BEATS {(Rock, Scissors), (Scissors, Paper), (Paper Rock)}: We may extend the relation above to "beats or is equal to" in the natural way. Determine whether the relation "beats or is equal to" on A is reflexive, transitive, symmetric, or antisymmetric. Is "beats or is equal to" a partial order? What happens if you try to draw a Hasse diagram for this relation?

Explanation / Answer

First define the extended relation R : 'BEATS or is equal to' as

R = {(Rock,Rock),(Scissors,Scissors),(Paper,Paper),(Rock,Scissors),(Scissors,Paper),(Paper,Rock)}.

Then the relation R is clearly reflexive, antisymmetric, but not symmetric and transitive.

So, it is not a partial order. Hence, a Hasse diagram can not be drawn.

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