For each language, if it is recognizable, describe a TM which recognizes it$.$ If it is not recognizable, prove that it isn't, using a reduction from any of HALTS$($TM$,$x$),$ ACCEPTS$($TM$,$ x$),$ EQUAL$\_$TM$($TM$1,$ TM$2),$ REG$\_$TM$($TM$),$ EQUAL$\_$CFG$($CFG$1,$ CFG$2),$ ALL$\_$CFG$($CFG$),$ and EMPTY$\_$TM$($TM$).$

Let $L2=\{\begin{array}{c}|\end{array}$ there does not exist i such that DFA accepts $\{$:$x^i\}.$