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Positively Contra

Posted in Test Prep on July 31, 2009 by

ContraIt is practically impossible to prep for the LSAT without understanding conditionals, which are statements in the form “If X, then Y.” Throughout the test, you will be asked to interpret these statements and draw valid conclusions based on them. Consider this statement:

If something is a bird, then it has wings.

According to this statement, it is always the case that birds have wings. For the purposes of the LSAT, it does not matter whether this statement is true. It matters a great deal, however, what can be logically concluded from this statement.

We use an arrow to represent the logical relationship between the two parts of the conditional.

“If it is a bird, then it has wings” can be symbolized:

B ⇒ W

We can also translate this statement as “Birds require wings” or “In order for something to be a bird, that thing must have wings.” In other words, having wings is a necessary condition of being a bird.

So what happens if we find out that something does not have wings? Since having wings is a necessary condition of being a bird, if something does not have wings, we know that it cannot be a bird. We symbolize this as:

~W ⇒ ~B  Here the tilde (“~”) means “NOT.”

This statement is called the contrapositive. In order to create the contrapositive, you must reverse and negate both terms in the statement.

The contrapositive has the same truth value as the original conditional statement. In other words, if the original statement is true, the contrapositive must also be true.

If it is true, for example, that all bananas are fruit (B ⇒ F), then it must also be true that if an object is not fruit, then it is not a banana (~F ⇒ ~B).

Understanding the contrapositive will give you a tremendous advantage in the Logic Games and Logical Reasoning sections.

Good luck! Please let us know if you have any questions.