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

Question 162

Multiple Choice

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample.
-1. (?x) (Ax ? Bx) ? (?x) Cx
2) (?x) (Ax • ?Bx)
3) (?x) (Dx ? Bx) / (?x) (Dx ? Cx)


A) Valid
B) Invalid. Counterexample in a domain of 2 members, in which:
 Aa: True  Ba: False  Ca: False  Da: False  Ab: False Bb: True Cb: False  Db: True \begin{array} { l l l l } \text { Aa: True } & \text { Ba: False } & \text { Ca: False } & \text { Da: False } \\\text { Ab: False} &\text { Bb: True } &\text {Cb: False }&\text { Db: True } \\\end{array}
C) Invalid. Counterexample in a domain of 2 members, in which:
 Aa: True  Ba: False  Ca: False  Da: False  Ab: True Bb: True Cb: True  Db: True \begin{array} { l l l l } \text { Aa: True } & \text { Ba: False } & \text { Ca: False } & \text { Da: False } \\\text { Ab: True} &\text { Bb: True } &\text {Cb: True }&\text { Db: True } \\\end{array}
D) Invalid. Counterexample in a domain of 2 members, in which:
 Aa: False Ba: False  Ca: False  Da: False  Ab: False Bb: True Cb: False  Db: True \begin{array} { l l l l } \text { Aa: False} & \text { Ba: False } & \text { Ca: False } & \text { Da: False } \\\text { Ab: False} &\text { Bb: True } &\text {Cb: False }&\text { Db: True } \\\end{array}
E) Invalid. Counterexample in a domain of 2 members, in which:
Aa: True Ba: False Ca: False Da: False Ab: True Bb: False Cb: False Db: True

Correct Answer:

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