Final answer:
In Baze v. Rees, the Supreme Court rejected the argument that the use of lethal injection constitutes cruel and unusual punishment, hence upholding the constitutionality of the execution method under the Eighth Amendment.
Step-by-step explanation:
In Baze v. Rees, the argument made and rejected by the Court was A) Argument against the use of lethal injection as cruel and unusual punishment. The Supreme Court upheld the constitutionality of the three-drug cocktail used for executions by lethal injection, ruling that it does not violate the Eighth Amendment's ban on cruel and unusual punishments.
The case revolved around the claim that the protocol for lethal injection in Kentucky, which was similar to that used by many states, could not reliably produce unconsciousness and thus might cause undue suffering. However, the Supreme Court found that the plaintiffs failed to prove a substantial risk of serious harm and did not present a viable alternative method that would significantly reduce that risk, which led to the rejection of the claim. This decision has had a significant impact on how the death penalty is administered in the United States.