Hi, these are two questions from the argument compeletion drill, in the flashcard section

I was having trouble finding the missing premise; example 1. P: Y=>C Not C => Not Y P: ? P: A => not B B => Not A C: B => C Not C => Not B example 2 : P: D=> A Not A => Not D P: C => D Not D => Not C P: ? C: Not X => A Not A => X

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Irina September 20, 2019

@jbelcher,

Let's look at these examples. It is not necessary to write out the contrapositive of every premise, rather look for common elements:

(1) Y -> C
(2) ?
(3) A -> ~B
(4) Therefore, B -> C

Let's start by taking a contrapositive of (3) to match it with B in the conclusion:

(5) B -> ~A

Now, how do we get from B -> ~ A to B -> C, we need to connect ~A to C. Per (1) Y -> C, thus the missing premise must be ~A - > Y.

Taken together these premises will result in the following chain:

B-> ~A
~A -> Y
Y-> C

B-> ~A -> Y-> C

Therefore, B-> C.

For example 2:

(1) D ->A
(2) C ->D
(3) ?
(4) Therefore, ~X -> A

Note that (1) and (2) have a common element D, thus we can make the following inference from (1) and (2):

C -> A

Now how do we make an inference from C->A to our conclusion ~X -> A, we need to connect ~X and C:

~X -> C

The resulting premises:
~X -> C
C -> A

allow us to infer the conclusion:

~X -> A .

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