select a counterexample for the given invalid argument.
-1. (∀x)(Kx $ \lor $ Lx)
2) (∃x)∼Kx / (∀x)Lx
A) Counterexample in a domain of 2 members, in which: Ka: True La: True
Kb: False Lb: True
B) Counterexample in a domain of 2 members, in which: Ka: True La: False
Kb: True Lb: True
C) Counterexample in a domain of 2 members, in which: Ka: True La: True
Kb: True Lb: True
D) Counterexample in a domain of 2 members, in which: Ka: False La: False
Kb: False Lb: False
E) Counterexample in a domain of 2 members, in which: Ka: True La: False
Kb: False Lb: True

Question

Quizplus · Accepted Answer

The argument is invalid because it assumes that if there exists an x for which Kx is not true, then Lx must be true for all x. However, the counterexample E shows a scenario where for one member, K is not true and L is also not true, which contradicts the conclusion that for all x, Lx must be true if there exists an x for which Kx is not true. This demonstrates that the existence of an x that does not satisfy Kx does not necessarily imply that all x satisfy Lx.

Select a Counterexample for the Given Invalid Argument ∨ \lor ∨

Select a Counterexample for the Given Invalid Argument $\lor$