Question: b and d Determine whether each argument is valid. If the argument is valid, give a proof using the laws of logic. If the argument

b and d

Determine whether each argument is valid. If the argument is valid, give a proof using the laws of logic. If the argument is invalid, give values for the predicates P and Q over the domain (a, b) that demonstrate the argument is invalid. 3x (P(x) A Q(x)) :: 3x Q(x) A 3X P(x) Solution (b) 3x Q(x) A 3X P(x) :- 3x (P(x) A Q(x)) VX (P(x) A Q(x)) VX Q(x) AVX P(x) Solution (d) Vx (P(x) v Q(x)) VX Q(x) v VX P(x)

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