Q17 - Punishment for crimes

[cobyerez79]

Is this a formal logic question? If yes, how would one diagram it?
And of course, how does c provide the correct answer?
Thanks

[sumukh09]

Yeah you can approach this one diagrammatically.

Premise 1:

Punishment deters ---> Punishment Justified

Premise 2:

~Punishment deters ie) it has been shown that punishment does not deter

Conclusion:

~Punishment Justified

This is what we call a mistaken negation. We can't negate the sufficient condition and negate the necessary condition as a result.

In the first premise, we have punishment justified as the necessary condition [Punishment deters ---> Punishment Justified]

But the conclusion says: ~Punishment deters ---> ~Punishment Justified; and the contrapositive of this is:
Punishment Justified ---> Punishment Deters

In other words, the necessary condition is mistaken for the sufficient condition -- which is what answer choice C says.