# X Unless Y – Formal Logic for LSAT Prep

By
Greg Smith

X unless Y

The easiest way to look at this statement is as

IF not X then Y
OR
IF not Y then X

You can pick either one of the terms (X or Y) place them first and negate that term or make it the opposite and place the other term second. (to negate or make opposite just means to change “X” to “not X” or to change “not X” to “X”)

So “Not A unless B” becomes

If A then B
OR
If not B then not A

The term you put first in the IF-THEN statement is turned to the opposite meaning “Not A” becomes “A” or “A” becomes “Not A”

You can also look at Unless as essentially the same as saying “IF NOT”

So X Unless Y is the same as “X IF Not Y” or “IF Not Y then X”

Let’s try this in a sentence.

I will go to the park unless I stay home.

This is the same as “I will go to the park if I do not stay home” or…

IF Not Home then Park
IF Not Park then Home

Here’s some more practice statements translated into IF-THEN statements.

A unless B

If not A then B
If not B then A

Unless you apply the brakes, you will crash.

If Not Crash then Braked
If Not Braked then Crashed

You will fail this exam unless you study for it.

If Not Study then Fail
If Not Fail then Study

Note that as with your simple IF-THEN statements you cannot determine any additional information from theses statements. For example:

A unless B

Gives you:

If Not B then A
If Not A then B

But does not tell you anything if you are given A or B.

If A then ???
If B then ???

September 21, 2009

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