Finish Part 3

assignments/a2/a2.tex

@@ -111,7 +111,7 @@ $\forall s \in sc.sections,~ ...$
 % TODO: fill in the predicate definition for two meeting times conflicting
 
 \begin{align*}
-MeetingTimesConflict(m_1, m_2) : TODO
+MeetingTimesConflict(m_1, m_2) : m_1[0] == m_2[0] \land m_1[2] > m_2[1] \land m_2[2] > m_1[1]
 \qquad \text{where $m_1, m_2 \in M$}
 \end{align*}
 
@@ -122,7 +122,8 @@ MeetingTimesConflict(m_1, m_2) : TODO
 % Use the MeetingTimesConflict predicate in your response.
 
 \begin{align*}
-SectionsConflict(s_1, s_2) : TODO
+SectionsConflict(s_1, s_2) : ('Y' \in \{s_1[1], s_2[1]\} \lor s_1[1] = s_2[1]) \Rightarrow \\
+\exists m_1 \in s_1[2], \text{ s.t. } \exists m_2 \in s_2[2], \text { s.t. } MeetingTimesConflict(m_1, m_2)
 \qquad \text{where $s_1, s_2 \in S$}
 \end{align*}
 
@@ -133,7 +134,7 @@ SectionsConflict(s_1, s_2) : TODO
 % Use the SectionsConflict predicate in your response.
 
 \begin{align*}
-IsValidSchedule(sc) : TODO
+IsValidSchedule(sc) : \forall s_1, s_2 \in sc.sections, SectionsConflict(s_1, s_2) \Rightarrow s_1 = s_2
 \qquad \text{where $sc \in SC$}
 \end{align*}
 
@@ -157,7 +158,7 @@ Note that a course $c \in C$ is a tuple, and $c[2]$ is a set of sections, and so
 % TODO: fill in the predicate definition for a section being compatible with a schedule.
 
 \begin{align*}
-IsCompatibleSection(sc, s) : TODO
+IsCompatibleSection(sc, s) : \forall s_1 \in sc.sections, \neg SectionsConflict(s, s_1)
 \qquad \text{where $sc \in SC, s \in S$}
 \end{align*}
 
@@ -168,7 +169,7 @@ IsCompatibleSection(sc, s) : TODO
 % Use IsCompatibleSection in your response.
 
 \begin{align*}
-IsCompatibleCourse(sc, c) : TODO
+IsCompatibleCourse(sc, c) : \exists s \in c[2] \text{ s.t. } IsCompatibleSection(sc, s)
 \qquad \text{where $sc \in SC, c \in C$}
 \end{align*}