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

question 55

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

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