The minters expansion of $$f\left( {P,Q,R} \right) = PQ + Q\overline R + P\overline R $$ is

What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?

The Boolean expression for the output $$f$$ of the multiplexer shown below is

Suppose the predicate $$F(x,y,t)$$ is used to represent the statements that person $$x$$ can fool person $$y$$ at time $$t$$. Which one of the statements below expresses best the meaning of the formula $$\forall x\exists y\exists t\left( {\neg F\left( {x,y,t} \right)} \right)?$$