To deduce is to draw a specific conclusion from a general principle. To induce is to derive a general principle from specific observations. The distinction extends to the verbs‘ corresponding nouns, deduction and induction, and they’re the basis of what we mean when we say deductive or inductive reasoning (though a philosopher or logician might rightly point out there is much more to these terms).
A simple example: Because all animals with hair are mammals, we can deduce that the furry animal outside is a mammal. And because every mammal we’ve ever seen has hair, we might induce that all mammals have hair. Inductions are often questionable as they are usually very broad, general statements, but they provide useful starting points for experiments. Deductions are more often correct because they make specific claims based on sound principles.
Induct means to admit as a member or to place in a position. Though its root is different from that of induce, induction is the corresponding noun of both. A similar linguistic oddity appears with deduce and deduct (meaning to take away); the words’ roots are different, but deduction corresponds to both.
In practical use, deduce appears more often than induce in senses related to drawing conclusions. Induce appears much more often in its other senses, including (1) to lead to a course of action, and (2) to bring about or stimulate the occurrence of—for example:
Will three bulging-brained telepaths induce you to buy the latest limited-edition Star Trek posters from Mondo? [Wired]
So just how much of a unique, unrepeatable event is the tsunami-induced nuclear crisis at Fukushima? [Telegraph]
And because induce is so seldom seen in its logic-related sense (outside writing discussing logic or philosophy), many writers simply use deduce in its place. For example, according to the words’ conventional meanings, induce would make more sense than deduce in these sentences:
Anytime there’s a bad female standup somewhere, some dickhead Interblogger will deduce that “women aren’t funny”. [Guardian]
Another discusses how humans are prone to using logic to deduce the great mystery of existence. [The Province]