$3.$ Study the ladder logic program in Figure $6-61,$ and answer the questions that follow a$.$ Under what condition will the latch rung $1$ be TRUE $?$ b $.$ Under what conditions will the unlatch rung $2$ be TRUE $?$ c $.$ Under what condition will rung $3$ be TRUE $?$ d $.$ When PL$1$ is on $,$ the relay is in what state $($ LATCHED or UNLATCHED $)?$ e $.$ When PL$2$ is on $,$ the relay is in what state $($ LATCHED or UNLATCHED $)?$ f $.$ Assume the relay is in its LATCHED state and all three inputs are FALSE $.$ What input change $($ s $)$ must occur for the relay to switch into its UNLATCHED state $?$ g $.$ If the examine if closed instructions at addresses $1/1,1/2,$ and $1/3$ are all TRUE $,$ what state will the relay remain in $($ LATCHED or UNLATCHED $)?$