Consider this statement in first$-$order predicate calculus for the following two questions:

vXvY hangsOutWith$$X$,$ Y$^$aZ $$infectedWith$$X$,$Z$^->$ infectedWith$$Y$,7^$

$->$ likelyToGetInfectedWith$(1,2)$

$40.$ Which of the following is the correct clausal form representation of this statement?

a$.-$ hangsOutWith $($X$,$ Y$)$ v $-$ infectedWith$($X$,$ f$($X$,$Y$))$ v infectedWithY, f$($X$,$Y$))$ v $($X $=$ Y$)$

V likelyToGetInfectedWith$($Y$,$ f$($X$,$ Y$))$

b$.-$ hangsOutWith $($X$,$ Y$)$ v $-$ infectedWith$($X$,$ Z$)$ v infectedWith$($Y$,$ Z$)$ v $($X $=$

Y$)$ v likelyToGetInfectedWith$($Y$,$ Z$)$

c$.$ likelyToGetInfectedWith$($Y$,2)=$ VX VY hangsOutWith $($X$,$ Y$)^3$ Z $($infectedWith$($X$,$ Z$)^$

$-$ infectedWith$($Y$,$ Z$)^-($X $=$ Y$))$

d$.-$ hangsOutWith $($X$,$ Y$)^-$ infectedWith$($X$,$ f$($X$,$Y$))^$ infectedWith$($Y$,$ f$($X$,$ Y$))^($X $=$ Y$)$

$^$ likelyToGetInfectedWith$($Y$,$ f$($X$,$Y$))$

e$.$ hangsOutWith $($X$,$ Y$)$ v infectedWith$($X$,$ Z$)$ v $-$infectedWith$($Y$,$ Z$)$ v $-($X $=$ y$)$

v likelyToGetInfectedWith$($Y$,$ Z$)$

$41.$ Which of the following is the correct Horn clause representation of this statement?

a$.$ There is no Horn clause representation of this statement.

b$.$ likelyToGetInfectedWith$($Y$,$ f$($X$,$ Y$)$ v infectedWith$($Y$,$ f$($X$,$Y$))$ v $($X$=$ Y$)-$ hangsOutWith IX$,$

Y$)^$ infectedWith$($X$,$ f$($X$,$ Y$))$

c$.$ likelyToGetInfectedWith$($Y$,$ Z$)=$ VX VY hangsOutWith $($X$,$ Y$)^$ aZ $($infectedWith$($X$,$ Z$)^$

$-$ infectedWith$($Y$,$ Z$)^-($X $=$ Y$))$

d$.$ likelyToGetInfectedWith$($Y$,$ f$($X$,$Y$))$ v infectedWith$($X$,$ f$($X$,$Y$))$ v $($X $=$ Y$)=-$ hangsOutWith $($X$,$

Y$)^$ infectedWith$($Y$,$ f$($X$,$Y$))^-$ infectedWith$($X$,$ f$($X$,$ Y$)$

e$.$ likelyToGetInfectedWith$($Y$,$Z$)=$ hangsOutWith $($X$,$ Y$)^($infectedWith$($X$,$ f$($X$,$ Y$))$ A

$-$ infectedWith$($Y$,$ f$($X$,$ Y$))^-($X $=$ Y$))$