🚧 Setup for 3.4

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tomit4 2026-06-06 00:40:18 -07:00
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@ -112,3 +112,28 @@ c. may be true or may be false.
c is the answer, it may be true or false depending on the nature of the property
involving $x$, and $y$. In other words, it relies on what $P(x, y)$ states.
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**Test Yourself**
Page 179
1. The rule of universal instantiation says that if some property is true for
_______ in a domain, then it is true for _______.
2. If the first two premises of universal modus ponens are written as "If $x$
makes $P(x)$ true, then $x$ makes $Q(x)$ true" and "For a particular value of
$a$ _______ , " then the conclusion can be written as "______. "
3. If the first two premises of universal modus tollens are written as "If $x$
makes $P(x)$ true, then $x$ makes $Q(x)$ true" and "For a particular value of
$a$ _______ ," then the conclusion can be written as " _______. "
4. If the first two premises of universal transitivity are written as "Any $x$
that makes $P(x)$ true makes $Q(x)$ true" and "Any $x$ that makes $Q(x)$ true
makes $R(x)$ true," then the conclusion can be written as "_______."
5. Diagrams can be helpful in testing an argument for validity. However, if some
possible configurations of the premises are not drawn, a person could
conclude that an argument was _______ when it was actually _______.