Provided that the premises are true (and that there are no other, external factors to consider), deductive inferences are necessary true.
If it is raining, [then] the road gets wet. It is raining. Therefore, the road gets wet.
A core property of formal systems, such as mathematics or logic is that they are based (almost) exclusively on deductive reasoning. This can also be interpreted as: everything that can be expressed by deduction will sooner or later be end up to be represented in a formal system. Either way, practical examples of deductive reasoning can be found precisely in areas where logic and mathematics plays a major role.
Typical examples from the mathematics textbook are in fact also examples of deductive logic (the general rule from which the result is deduced is inserted in square brackets):
Peter has 5 apples.
He eats one of those apples.
[and 5 minus 1 equals 4]
Therefore, Peter now has 4 apples left.
Practical applications of mathematics can of course also be found in engineering sciences. The following example illustrates this:
In bridge construction, the load-bearing capacity of a bridge is calculated on the basis of known physical laws (such as the law of the lever) and the known physical properties of the building materials. The results can be derived (with an added tolerance and valid only under certain conditions) by deduction from the known data and laws.
- Deductive reasoning on Wikipedia