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$4.$ For predicate $$ and statement $,$ let $(,).$ For each of the following, decide whether it is true or false

then justify your answer briefly.

a$.\{\}\{\}$

b$.$ There exists some $$ such that $\{\}\{\}.$

c$.$ For each state $,$ we have that $(,).$

d$.$ If $(,),$ then $.$

e$.$ If $,$ then $\{\}\{\}$