1. consider the followi axiomatic system: A1: Each bot pats exactly 2 tobs. A2: For each...

1. consider the followi axiomatic system:

A1: Each bot pats exactly 2 tobs.

A2: For each pair of distinct tobs, there is a bot that pats both tobs.

A3: There are exactly 5 tobs.

(a) Pick one of the three axioms and prove that it is independent from the other axioms in the system. Be sure to justify your answer.

(b) Find the minimum number of bots present in a model for this system. Be sure to justify your answer using the axioms given above.

Expert Solution

Answer:

a)

To show independence the easiest is axiom 3.

Let's take the following model. Here, black vertices replicate bots, white vertices replicate tobs, and there is an edge between a bot and a tob precisely when the bot pats that tob.

b)

lets take the Claim: There are atleast 10 bots

orchestra answered 1 year ago

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