P: X → AP: C → not ZP: not Z → not AC: ?

ReganMc October 1, 2019

More help needed

I don't know how I got that one right. I need more practice work, here. If possible

Create a free account to read and take part in forum discussions.

Already have an account? log in

Irina October 1, 2019

@ReganMc,

Is there a specific rule of inference that you are having trouble with?

This argument has three premises:
(1) X ->A
(2) C-> ~Z
(3) ~Z -> ~A

We can start by tracking a contrapositive of premise (1) so we have a common variable ~A in premises (1) and (3). The contrapositive of (1) is:

(4) ~A -> ~X

We can then combine the resulting premise (4) with premise (3) to form the following chain:

~Z -> ~A -> ~X ,which is equivalent to:
(5) ~Z -> ~X

Now we can combine the resulting premise (5) and premise (2) into the following chain:

C -> ~Z -> ~X which is equivalent to our conclusion:

Therefore, C -> ~X

Let me know if this makes sense and if you have any further questions.