Recall the aircraft collision avoidance system from the lecture. It takes the following inputs:

\(v_\text {own}\), which is the velocity of the aircraft in km/s.
\(v_\text {int}\), which is the velocity of the intruding aircraft in km/s.
\(\rho\), distance between the aircrafts in km.
\(\theta\), the direction from which the intruder approaches ownship in degrees.
\(\psi\), the direction of navigation of the intruder in degrees.

The aircraft collision system is a controller, which recommends actions based on a NN that has five output nodes: clear of conflict \(\text {COC}\), weak right \(\text {WR}\), strong right \(\text {SR}\), weak left \(\text {WL}\), or strong left \(\text {SL}\). The controller recommends one of five actions, based on which output node has the largest value. More specifically,
\(\text {ctrl}(\text {WL},\text {SL},\text {COC},\text {WR},\text {SR}) \equiv \begin {cases} \text {DO-WL}, & \text { if } \text {WR}< \text {WL}\wedge \text {SR}< \text {WL}\wedge \text {COC}< \text {WL}\wedge \text {SL}< \text {WL}\\ \text {DO-SL}, & \text { if } \text {WR}< \text {SL}\wedge \text {SR}< \text {SL}\wedge \text {WL}< \text {SL}\wedge \text {COC}< \text {SL}\\ \text {DO-WR}, & \text { if } \text {WL}< \text {WR}\wedge \text {SL}< \text {WR}\wedge \text {COC}< \text {WR}\wedge \text {SR}< \text {WR},\\ \text {DO-SR}, & \text { if } \text {WL}< \text {SR}\wedge \text {SL}< \text {SR}\wedge \text {COC}< \text {SR}\wedge \text {WL}< \text {SR}\\ \text {DO-COC}, & \text { otherwise.} \end {cases}\)
Formally specify property \(\phi _5\) which states that if the intruder is near and approaching from the left, the network advises strong right.