## 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} : ciRcj 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.**