$6.$ For the relation systems in Example $2\mathrm{.}6,$ determine which of the fol$-$

lowing mappings are representations. Explain your answers in terms of the representation condition.

a$.$

b$.$

c$.$

d$.$

$7.$ Suppose that we could classify every sotware failure as either a$)$

syntactic, b$)$ semantic, or c$)$ system crash. Suppose additionally that

M$($each delayed response$)=6$; M$($each incorrect output$)=6$; M$($each data$-$loss$)=69$

M$($each delayed response$)=1$; M$($each incorrect output$)=2$; M$($each data$-$loss$)=3$

M$($each delayed response$)=6$; M$($each incorrect output$)=3$; M$($each data$-$loss$)=2$

M$($each delayed response$)=0$; M$($each incorrect output$)=1$; M$($each data$-$loss$)=0\mathrm{.}5$