Three ways of thinking that it’s definitely worth getting your head around. Not the best descriptions of each I’ve ever read, but conveniently, all three on one Wikipedia page:
Deductive reasoning (deduction) allows deriving b from a only where b is a formal logical consequence of a. In other words, deduction derives the consequences of the assumed. Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. For example, given that all bachelors are unmarried males, and given that this person is a bachelor, one can deduce that this person is an unmarried male.
(Use deduction to work out or optimise, the answer)
Inductive reasoning (induction) allows inferring b from a, where b does not follow necessarily from a. a might give us very good reason to accept b, but it does not ensure b. For example, if all swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable. We have good reason to believe the conclusion from the premise, but the truth of the conclusion is not guaranteed. (Indeed, it turns out that some swans are black.)
(Use induction to take action in the absence of one answer)
Abductive reasoning (abduction) allows inferring a as an explanation of b. Because of this inference, abduction allows the precondition a to be abduced from the consequence b. Deductive reasoning and abductive reasoning thus differ in the direction in which a rule like “a entails b” is used for inference. As such, abduction is formally equivalent to the logical fallacy of affirming the consequent (or Post hoc ergo propter hoc) because of multiple possible explanations for b. For example, in a billiard game, after glancing and seeing the eight ball moving towards us, we may abduce that the cue ball struck the eight ball. The strike of the cue ball would account for the movement of the eight ball. It serves as a hypothesis that explains our observation. Given the many possible explanations for the movement of the eight ball, our abduction does not leave us certain that the cue ball in fact struck the eight ball, but our abduction, still useful, can serve to orient us in our surroundings. Despite many possible explanations for any physical process that we observe, we tend to abduce a single explanation (or a few explanations) for this process in the expectation that we can better orient ourselves in our surroundings and disregard some possibilities.
(Use abduction to prepare answers before you need them)