PART a
All Real Libraries Are Buildings Containing Books

Essay

PART A
All real libraries are buildings containing books, so some presidential libraries are not real libraries, since some buildings containing books are not presidential libraries.
The form of this argument is: a. $\begin{array} { l } \text {Some \( P \) are not \( \mathrm{R} \). }\\ \text {Some \( B \) are not \( P \). }\\ \hline\text {All R are B. }\\\end{array}$$\quad$ b. $\begin{array} { l } \text {Some \( P \) are not \( R \). }\\ \text {All R are \( \mathrm{B} \). }\\ \hline\text {Some \( B \) are not \( P \). }\\\end{array}$$\quad$ c. $\begin{array} { l } \text {Some B are not \( P \). }\\ \text { Some \( P \) are not \( R \).}\\ \hline\text { All \( \mathrm{R} \) are \( \mathrm{B} \).}\\\end{array}$

d. $\begin{array} { l } \text {All R are B. }\\ \text {Some P are not R. }\\ \text {Some B are not P. }\\\end{array}$$\quad$ e. $\begin{array} { l } \text {All R are \( \mathrm{B} \). }\\ \text {Some \( B \) are not. \( P \). }\\ \text {Some P are not R. }\\\end{array}$ PART B
Which of the following substitutions proves the argument invalid?
A) R = mammals, B = animals, P = cats.
B) B = mammals, P = cats, R = dogs.
C) P = animals, R = cats, B =mammals.
D) R = fish, B = animals, P = dogs.
E) B = fish, R = animals, P = cats.