Logical Opposition

The concept of logical opposition appears frequently on the LSAT in a variety
of forms. A complete knowledge of the logical opposites that most often appear
will provide you with a framework that eliminates uncertainties and ultimately
leads to skilled LSAT performance. Consider the following question:
What is the logical opposite of sweet?
Most people reply “sour” to the above question. While “sour” is an opposite of
“sweet,” it is considered the polar opposite of “sweet,” not the logical opposite.
A logical opposite will always completely divide the subject under
consideration into two parts. Sweet and sour fail as logical opposites since tastes
such as bland or bitter remain unclassified. The correct logical opposite of
“sweet” is in fact “not sweet.” “Sweet” and “not sweet” divide the taste
spectrum into two complete parts, and tastes such as bland and bitter now
clearly fall into the “not sweet” category. This same type of oppositional
reasoning also applies to other everyday subjects such as color (what is the
logical opposite of white?) and temperature (what is the logical opposite of
hot?).
To help visualize pairs of opposites within a subject, we use an Opposition
Construct. An Opposition Construct efficiently summarizes subjects within a
limited spectrum of possibilities, such as quantity:

In this quantity construct, the range of possibilities extends from All to None.
Thus, these two “ends” are polar opposites. There are also two pairs of logical
opposites: All versus Not All and Some versus None. These logical opposites
hold in both directions: for example, Some is the precise logical opposite of
None, and None is the precise logical opposite of Some. The relationship
between the four logical possibilities of quantity becomes more complex when
we examine pairs such as Some and All. Imagine for a moment that we have
between 0 and 100 marbles. According to the above construct, each logical
possibility represents the following:

By looking closely at the quantities each possibility represents, we can see that
Some (1 to 100) actually includes All (100). This makes sense because Some, if
it is to be the exact logical opposite of None, should include every other
possibility besides None. The same relationship also holds true for Not All
(0 to 99) and None (0).
The relationship between Some and Not All is also interesting. Some (1 to 100)
and Not All (0 to 99) are largely the same, but they differ significantly at the
extremes. Some actually includes All, the opposite of Not All, and Not All
includes None, the opposite of Some. As a point of definition Not All
is the same as Some Are Not.
The same line of reasoning applies to other subjects that often appear on the
LSAT:

The Time and Space constructs are very similar to the Quantity construct. For
example, Always is somewhat equivalent to “All of the time.” Everywhere
could be said to be “All of the space.” Thus, learning one of these constructs
makes it easy to learn the other two.