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

question 38

Multiple Choice

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample.
-1. (?x) (Gx ? Hx)
2) (?x) (Gx • Ix)
3) (?x) (Gx • Jx)
4) (?x) (Jx ? Hx) / (?x) (Ix • Jx)

• A) Valid
• B) Invalid. Counterexample in a domain of 1 member, in which:
• \[\begin{array} { l l l l }
• \text { Ga: True } & \text { Ha: True } & \text { Ia: True } & \text { Ja: True } \\
• \text { Gb: True} &\text { Hb: True } &\text {Ib: True }&\text { Jb: True } \\
• \end{array}\]
• C) Invalid. Counterexample in a domain of 1 member, in which:
• \[\begin{array} { l l l l }
• \text { Ga: False } & \text { Ha: True } & \text { Ia: True } & \text { Ja: True } \\
• \text { Gb: True} &\text { Hb: True } &\text {Ib: True }&\text { Jb: False } \\
• \end{array}\]
• D) Invalid. Counterexample in a domain of 1 member, in which:
• \[\begin{array} { l l l l }
• \text { Ga: True } & \text { Ha: True } & \text { Ia: True } & \text { Ja: True } \\
• \text { Gb: True} &\text { Hb: True } &\text {Ib: True }&\text { Jb: False } \\
• \end{array}\]
• E) Invalid. Counterexample in a domain of 1 member, in which:
• \[\begin{array} { l l l l }
• \text { Ga: False } & \text { Ha: True } & \text { Ia: False } & \text { Ja: False } \\
• \text { Gb: False } &\text { Hb: True } &\text {Ib: True }&\text { Jb: False } \\
• \end{array}\]

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