I have a Math problem where I have some true statements, and I want to know if there is a feasible solution to an equation. I would like to know how to do that in either Matlab or Mathematica.

The true statements are:

```
0 < a, b, c, d, e
a, b, c integers
a < b < c
d*b + e*b > e * c
```

I want to know that, if given those conditions, it is possible to find values for `a`

, `b`

, `c`

, `d`

, `e`

, such that the following inequality holds:

```
d*a > d*b +e*b - e*c
```

Answer:

I think the Reduce function in Mathematica is the appropriate tool for this.

```
Reduce[d*a > d*b + e*b + e*c && a > 0 && b > 0 && c > 0 && d > 0 && e > 0 && d*b + e*b > e*c && a < b < c, {a, b, c, d, e}, Integers]
```

this yields `False`

meaning it cannot be satisfied as formulated. However, relaxing the a < b < c constraint does yield a (set of) solution.

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