An airline service the five cities c1​,c2​,c3​,c4​, and c5​. Table below gives the cost (in dollars) of going from ci​ to cj​. Thus, the cost of going from c1​ to C3​ is $100, while the cost of going from c4​ to c2​ is $200. Define the following relation R on the set of cities A={c1​,C2​,C3​,C4​,C5​} : ci​Rcj​ if and only if the cost of going from ci​ to cj​ is defined and less than or equal to $180. Find R.

Question

An airline service the five cities c1​,c2​,c3​,c4​, and c5​. Table below gives the cost (in dollars) of going from ci​ to cj​. Thus, the cost of going from c1​ to C3​ is $100, while the cost of going from c4​ to c2​ is $200. Define the following relation R on the set of cities A={c1​,C2​,C3​,C4​,C5​} : ci​Rcj​ if and only if the cost of going from ci​ to cj​ is defined and less than or equal to $180. Find R.

Answer

To find R, we need to identify all pairs of cities (ci, cj) where the cost of travel is defined (not “-“) and less than or equal to $180, based on the given table.

Here are the pairs that satisfy this condition:

  • (c1, c3) : Cost = $100
  • (c1, c4) : Cost = $150
  • (c2, c1) : Cost = $120
  • (c2, c3) : Cost = $180
  • (c3, c1) : Cost = $160
  • (c3, c2) : Cost = $140
  • (c3, c4) : Cost = $180
  • (c4, c1) : Cost = $130

Therefore, the relation R is:

R = {(c1, c3), (c1, c4), (c2, c1), (c2, c3), (c3, c1), (c3, c2), (c3, c4), (c4, c1)}

This represents all the city pairs connected by flights costing $180 or less.

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