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1. (8 points) Given the following definitions: - K : the domain of all people who love kung fu competitions - M : the domain of all martial artists. - S(x):x is stressed. - T(x,y) : person x has talked to martial artist y. In each of the two cases below, determine whether or not the two predicate logic statements given are logically equivalent. If the two propositions are logically equivalent, explain why. If they are not logically equivalent, then give an example where their truth values differ, and explain why they differ. (a) (4 points) xK,yM,T(x,y)S(x)xK,(yM,T(x,y))S(x) (b) (4 points) xK,yM,T(x,y)S(x)xK,(yM,T(x,y))S(x).

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1. (8 points) Given the following definitions: - K : the domain of all people who love kung fu competitions - M : the domain of all martial artists. - S(x):x is stressed. - T(x,y) : person x has talked to martial artist y. In each of the two cases below, determine whether or not the two predicate logic statements given are logically equivalent. If the two propositions are logically equivalent, explain why. If they are not logically equivalent, then give an example where their truth values differ, and explain why they differ. (a) (4 points) xK,yM,T(x,y)S(x)xK,(yM,T(x,y))S(x) (b) (4 points) xK,yM,T(x,y)S(x)xK,(yM,T(x,y))S(x)

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