Question 26
**Form I.** Consider the statements
$$
\begin{aligned} (1)\quad&p\land\neg q\land r,\\ (2)\quad&\neg p\land\neg q\land r,\\ (3)\quad&p\land\neg q\land\neg r,\\ (4)\quad&\neg p\land q\land r, \end{aligned}
$$
where $p,$ $q,$ $r$ are propositions. How many of these imply the truth of $(p\to q)\to r?$
**Form II.** Consider the statements $(1)$ $p$ and $r$ are true and $q$ is false, $(2)$ $r$ is true and $p$ and $q$ are false, $(3)$ $p$ is true and $q$ and $r$ are false, $(4)$ $q$ and $r$ are true and $p$ is false. How many of these imply the truth of the statement “$r$ is implied by the statement that $p$ implies $q$”?
$$
\begin{aligned} (1)\quad&p\land\neg q\land r,\\ (2)\quad&\neg p\land\neg q\land r,\\ (3)\quad&p\land\neg q\land\neg r,\\ (4)\quad&\neg p\land q\land r, \end{aligned}
$$
where $p,$ $q,$ $r$ are propositions. How many of these imply the truth of $(p\to q)\to r?$
**Form II.** Consider the statements $(1)$ $p$ and $r$ are true and $q$ is false, $(2)$ $r$ is true and $p$ and $q$ are false, $(3)$ $p$ is true and $q$ and $r$ are false, $(4)$ $q$ and $r$ are true and $p$ is false. How many of these imply the truth of the statement “$r$ is implied by the statement that $p$ implies $q$”?