Rule of Universal Specification
This is a fairly obvious rule, but one that is important:
If an open statement is true for all possible replacements in the
designated universe, then that open statement is true for each
specific individual member in that universe.
Symbolically speaking, we have:
If
2200
x p(x) is true, then we know that p(a) is true, for each a in
the universe for x.
Here is a simple example using this rule. Consider the
following premises:
1) All years divisible by 400 are leap years
2) 2000 is divisible by 400
Therefore, 2000 is a leap year.
Symbolically, consider setting up these three statements:
p(x): x is divisible by 400
q(x): x is a leap year
Now, the given information is
2200
x [p(x)
⇒
q(x)]
If we wish to determine the status of the current year, we add
into our premise the statement p(2000) as being true.
Using the Rule of Universal Specification, and Rule of
Detachment, we can conclude that q(2000) is true; that is 2000
is a leap year.
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Let’s go ahead and look at another example in greater detail.
Consider each of these open statements for the next example:
p(x): x is a show on primetime TV
q(x): x is a show on latenight TV
r(x): x is a soap opera
Now, consider the following argument:
No
soap opera is on primetime TV or latenight TV
All My Children is a soap opera.
Therefore, All My Children is not on primetime TV.
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 Spring '09
 Division, Parity, Evenness of zero

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