For each of the following (universes and) pairs of statements, use the Rule of Universal Specification, in conjunction with Modus Ponens and Modus Tollens, in order to fill in the blank line so that a valid argument results.
a) [The universe comprises all real numbers.]
All integers are rational numbers.
The real number n is not a rational number.
b) [The universe comprises the present population of the United States.]
All librarians know the Library of Congress Classification System.
∴ Margaret knows the Library of Congress Classification System.
c) [The same universe as in part (b).]
Sondra is an administrative director.
∴Sondra knows how to delegate authority.
d) [The universe consists of all quadrilaterals in the plane.]
All rectangles are equiangular.
∴ Quadrilateral MNPQ is not a rectangle.
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