# Using predicate logic, how to solve symmetric and anti reflexive

The networks is: A->B->C->D The channels used by the network are: lo, med, hi h-hi, l-lo, m-med

• i) A network uses one, and only one channel.
• ii) Networks within close proximity cannot both use the same channel.
• iii) “Close proximity” is an anti-reflexive, symmetric relation.
• Q1) Define a specification language to formally specify the requirements laid out above (predicate or propositional logic.

• Q2) In the specification language, and subject to the assumptions you have made, define the requirements with logical formulas:
• Q3) Extending your specification language if necessary, provide a set of requirements which, together with your answer to (2), ensures any satisfying model has the structure detailed here.

• For Q1, I have tried this
• Al - A uses channel lo, Ah - A uses channel hi, Am - A uses channel med.
• Bl - B uses channel lo, Bh - B uses channel hi, Bm - B uses channel med.
• Cl - C uses channel lo, Ch - C uses channel hi, Cm - C uses channel med.
• Dl - D uses channel lo, Dh - D uses channel hi, Dm - D uses channel med.
• For Q2, I have tried doing this
• i) (Al v Am V Ah) ^ (Bl v Bm v Bh) ^ (Cl v Cm v Ch) ^ (Dl v Dm v Dh)
• ii) ~((Al^Bl) v (Am^Bm) v (Ah ^ Bh)) ^ ~((Bl ^ Cl) v (Bm ^ Cm) v (Bh ^ Ch)) ^ ~((Cl^Dl) v (Cm^Dm) v (Ch ^ Dh))
• iii) I dont know how to go with this.