In an REF$615$ relay, the low set stage for undervoltage is set to $80$ V and the high set undervoltage is set to $50$ V; the low set overvoltage is set to $90$ V and high set overvoltage is set to $140$ V$.$ Nominal voltage for the relay is $120$ V$.$ Characteristic chosen for the low set stage undervoltage is A type with k$<=0\mathrm{.}7$ and characteristic chosen for the high set undervoltage is B type with k$<<=0\mathrm{.}2.$ Characteristic chosen for low and high set overvoltage is definite time with trip times respectively $2$ sec and $1$ sec$.$ Assume that a voltage of $30$ V is applied to the relay. Output PO$1($Normally Open$)$ is set to close when relay trips. Which setting caused the output to close? Choose one of the following options. $($show calculations and explain your answer on paper$).$

Group of answer choices

t$>$

t$<<$

t$<$

t$>>$