Consider the following argument for ethical relativism:

$1.$ The ethical judgments people make differ greatly, depending on where and when they live.

$2.$ If the ethical judgments people make differ greatly, then the ethical standards people use differ greatly.

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L$1$ The ethical standards people use differ greatly.

Therefore, ethical relativism is true.

Which of the following assessments is correct?

$1.$

The argument is not sound. It is logically valid; L$1$ can be derived from premises $1$ and $2$ by application of modus ponens, and the conclusion follows by modus ponens again from L$1.$ However, there is powerful evidence that the first premise is false.

$2.$

The argument is sound. It is logically valid; L$1$ can be derived from premises $1$ and $2$ by application of modus ponens, and the conclusion follows by modus ponens again from L$1.$ However, there is powerful empirical evidence that the first and second premises are true.

$3.$

The argument is sound. It is logically valid; L$1$ can be derived from premises $1$ and $2$ by application of modus ponens, and the conclusion follows by modus ponens again from L$1.$ However, the first premise is obviously true and the second premise is a logical truth.

$4.$

The argument is not sound. It is logically valid; L$1$ can be derived from premises $1$ and $2$ by application of modus ponens, and the conclusion follows by modus ponens again from L$1.$ However, there is powerful empirical evidence that the first and second premises are both true. Additionally, sociology has proven that ethical relativism is true.

$5.$

The argument is sound. It is logically valid; L$1$ can be derived from premises $1$ and $2$ by application of modus ponens, and the conclusion follows because it's a logically necessary truth. Morality is by definition relativistic and everyone knows it$.$

$6.$

The argument is not sound. It is logically invalid; L$1$ can be derived from premises $1$ and $2$ by application of modus ponens, but ethical relativism requires much more than that people merely use different ethical standards. Additionally, there is powerful evidence against the first premise, while the second premise faces counterexamples.