Validity or Invalidity How to prove validity of this since the conclusion does not seem to have any link with the premises? > Murder is always wrong > > Sometimes murder is not wrong > > Therefore, the death penalty should be illegal

To say an argument is valid is not to say the conclusion is true but to say the premises imply the conclusion.

So If you premises are $A=$ Murder is always wrong and $B = $ Murder is sometimes not wrong, and your conclusion is $C=$ Snails eat ping-pong balls. Then the argument is valid if $A \land B \implies C$ is true.

As $B = \lnot A$ and $A\land \lnot A$ is always false (no matter what $A$ is). And for any false statement $D$ then $D \implies C$ is always true (no matter what $C$ is).

So $(A \land \lnot A) \implies C$ is always true and

1) $A$ 2) $\lnot A$ Conc: $C$ is always valid. (But pretty dang useless.)