3. Stable Matchings. 2 points/part. In the following "favorite" partner means first on preference list, "optimal" partner means the most preferred partner in any stable pairing. 1. There is a stable pairing where no job is paired with the first candidate on their list. True O False 2. If there is a stable pairing where a job j is paired with its pessimal candidate, then all jobs are paired with their pessimal candidate in that stable pairing. O True O False 3. No job can improve their final outcome in the jobs propose matching algorithm by submitting a false preference list. True O False 4. No collection of jobs can conspire to improve the outcome of any job j in the jobs propose matching algorithm by jointly submitting false preference lists. True O False 5. If in a run of a jobs propose algorithm, job jis rejected by candidate c because of job j' then job j' can never be rejected by a candidated because of job j. True False