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

question 123

Multiple Choice

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample.
-1. (?x) (?y) (Pxy • ?Pyx)
2) (?x) [(?y) Pxy ? (?y) Qxy] / (?x) (?y) (Qxy • ?Pyx)

• A) Valid
• B) Invalid. Counterexample in a domain of three members, in which:
• \(\begin{array}{lll}
• \text { Paa: True } & \text { Pab: True } & \text { Pac: False } \\
• \text { Pba: False } & \text { Pbb: True } & \text { Pbc: True } \\
• \text { Pca: True } & \text { Pcb: False } & \text { Pcc: True } \\
• \text { Qaa: False } & \text { Qab: False } & \text { Qac: True } \\
• \text { Qba: True } & \text { Qbb:True } & \text { Qbc: True } \\
• \text { Qca: True } & \text { Qcb:True } & \text { Qcc: True }
• \end{array}\)
• C) Invalid. Counterexample in a domain of three members, in which:
• \(\begin{array}{lll}
• \text { Paa: True } & \text { Pab: True } & \text { Pac: False } \\
• \text { Pba: False } & \text { Fbb: False } & \text { Pbc: False } \\
• \text { Pca: False } & \text { Pcb: False } & \text { Pcc: True } \\
• \text { Qaa: False } & \text { Qab: False } & \text { Qac: True } \\
• \text { Qba: True } & \text { Qbb:True } & \text { Qbc: False } \\
• \text { Qca: True } & \text { Qcb: True } & \text { Qcc: True }
• \end{array}\)
• D) Invalid. Counterexample in a domain of three members, in which:
• \(\begin{array}{lll}
• \text { Paa: False } & \text { Pab: Ture } & \text { Pac: False } \\
• \text { Pba: False } & \text { Pbb: True } & \text { Pbc: True } \\
• \text { Pca: True } & \text { Pcb: True } & \text { Pcc: True } \\
• \text { Qaa: False } & \text { Qab:True } & \text { Qac: True } \\
• \text { Qba: False } & \text { Qbb:True } & \text { Qbc: True } \\
• \text { Qca: True } & \text { Qcb:True } & \text { Qcc: False }
• \end{array}\)
• E) Invalid. Counterexample in a domain of three members, in which:
• \(\begin{array}{lll}
• \text { Paa: True } & \text { Pab: True } & \text { Pac: False } \\
• \text { Pla: False } & \text { Pbb: False } & \text { Ploc: True } \\
• \text { Pca: True } & \text { Pcb: False } & \text { Pcc: True } \\
• \text { Qaa: False } & \text { Qab: False } & \text { Qac: True } \\
• \text { Qba: False } & \text { Qbb: False } & \text { Qbc: False } \\
• \text { Qca: True } & \text { Qcb: True } & \text { Qcc: False }
• \end{array}\)

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Definitions:

Continental Rift

A low trough or series of troughs bounded by normal faults, especially where two parts of a continent begin to rift apart.

Ocean-ocean Convergent

A tectonic boundary where two oceanic plates converge, leading to the subduction of one plate beneath the other and often resulting in volcanic island arcs.

Geologic Activity

A term that encompasses processes occurring within the Earth's crust and surface, including earthquakes, volcanic eruptions, and plate tectonics.

Plate Boundaries

The edges where two or more tectonic plates meet, characterized by geological activity such as earthquakes and volcanic eruptions.