To expound on @nefret's comment: Given that logic puzzles are becoming more popular on Sporcle, understanding the contrapositive is as important around here as learning to spell Kyrgyzstan. If an IF-THEN statement is true, then its contrapositive is always also true. Here's the contrapositive in its simplest Sporcle-ized form:
(IF a THEN b) --EQUALS-- (IF NOT b THEN NOT a)
There's also a similar relation called an inverse, which is where most of the confusion lies. While an IF-THEN statement's contrapositive is equivalent, its inverse is not. In other words, the following is not necessarily true:
(IF a THEN b) --EQUALS-- (IF NOT a THEN NOT b)
Assuming the truthfulness of an inverse is a common fallacy, and it's arguably been the cause of more logical errors (and lousy grades in Formal Logic college courses, trust me on that one) than any other fallacy in human history. Let's run through an example...
IF (a) something is a man THEN (b) that something is mortal
No arguments here, right? All men are mortal. Now, note that the contrapositive is pretty trivially true:
IF (not-b) something is immortal THEN (not-a) that something is not a man
But note that the inverse is not necessarily true, and in fact comically not so:
IF (not-a) something is not a man THEN (not-b) that something is immortal.
Our something might be a sheep, and your average sheep isn't immortal. Or it might be a tree, or a clock radio, or Kyrgyzstan. Or it might be Zeus, who isn't a man but is immortal, demonstrating that in some cases the inverse really is true. The key to keep in mind is this: if the original IF-THEN statement is true, then the contrapositive is always true, period, no exceptions. However, the inverse may or may not be true (and as such, is pretty much useless for use in Sporcle logic puzzles.) Carry on. |
Electoral Votes (All Time)
Country-Capital Ratios
The Sporcle Beatles Mystery
