a$)$ Use the predicate specifications:$[5+3=8$ Marks$]$s$($X$)$: X is a student p$($X$)$: X excels in physics h$($X$,$ Y$)$: X helps Yc$($X$)$: X struggles with chemistryand the constant symbols:$*$ Alice$*$ Bob$*$ Chesterto translate the following natural language statement into predicate logic:Some student, who excels in physics, helps Alice, who struggles with chemistry.b$)$ Consider the predicate logic formula:Va By Q$($r$,$ y$)^$ QG$)$ v $($Vz $($R$($z$,+)$ St$)))$ A Aw T$($w$,$ z$,$ w$)).$Identify a variable which has both free and bound occurrences in this formula. Mark the twooccurrences in the formula, the one where it is bound and the other where it is free. If there is no such vaniable for any part of the question, write no such variable exists.