# The author uses the word "immediacy" (line 39) most likely in order to express

Jasmin on September 17, 2019

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

Irina on 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.