Chapter 1.1, Problem 45E

Use Exercise 44 to construct a compound proposition that is true if and only if exactly one of the propositionsp₁,p₂, ...,p_nis true.

[Hint: Combine the compound proposition in Exercise 44 and a compound proposition that is true if and only if at least one ofp₁,p₂, ...,p_nis true.)

44. Ifp₁,p₂, ...,p_narenpropositions, explain why

   $\underset{i=1}{\overset{n-1}{\Lambda }}\underset{j=i+1}{\overset{n}{\Lambda }}\left(\neg p_i\vee \neg p_j\right)$

is true if and only if at most one ofp₁,p₂, ...,p_nis true.