Solved

Determine Whether the Given Argument Is Valid or Invalid D) Invalid

Question 69

Multiple Choice

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample.
-1. (?x) [Tx ? (?y) (Sy • Wxy) ]
2) (?x) (Sx • Vx)
3) (?x) (Tx • Rx) / (?x) [(Rx • Vx) • (?y) Wxy]


A) Valid
B) Invalid. Counterexample in a domain of one member, in which: Ta: True Sa: False Waa: True
Ra: False Va: True
C) Invalid. Counterexample in a domain of two members, in which:
 Ta: False  Sa: False  Waa: True  Tb: True  Sb: True  Wab: False  Ra: True  Va: False  Wba: False  Rb: False  Vb: False  Wbb:True \begin{array}{lll}\text { Ta: False } & \text { Sa: False } & \text { Waa: True } \\\text { Tb: True } & \text { Sb: True } & \text { Wab: False } \\\text { Ra: True } & \text { Va: False } & \text { Wba: False } \\\text { Rb: False } & \text { Vb: False } & \text { Wbb:True }\end{array}

D) Invalid. Counterexample in a domain of two members, in which:
 Ta: False  Sa: True  Waa: True  Tb: True  Sb: True  Wab: True  Ra: False  Va: False  Wba: False  Rb: False  Vb:True  Wbb: False \begin{array}{lll}\text { Ta: False } & \text { Sa: True } & \text { Waa: True } \\\text { Tb: True } & \text { Sb: True } & \text { Wab: True } \\\text { Ra: False } & \text { Va: False } & \text { Wba: False } \\\text { Rb: False } & \text { Vb:True } & \text { Wbb: False }\end{array}

E) Invalid. Counterexample in a domain of two members, in which:
 Ta: True  Sa: True  Waa: True  Tb: False  Sb: True  Wab: True  Ra: True  Va: False  Wba: True  Rb: False  Vb:True  Wbb: True \begin{array}{llll}\text { Ta: True } & \text { Sa: True } & \text { Waa: True } & \\ \text { Tb: False } & \text { Sb: True } & \text { Wab: True } \\ \text { Ra: True } & \text { Va: False } & \text { Wba: True } \\\text { Rb: False } & \text { Vb:True } & \text { Wbb: True }\end{array}

Correct Answer:

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