Identify what you can properly conclude from the given premises:P: A → MP: not X → JP: X → not MC: ?

Irina September 5, 2019

@taniyafoster,

Let's start by identifying common elements in the premises:

(1) A -> M
(2) X -> ~ M

How do we convert M to ~M?

A contrapositive of A -> M is ~ M -> ~A

We can then combine the resulting statement:

~ M -> ~A with
X -> ~ M

to form the following logical chain:
X-> ~M -> ~A

which is equivalent to X -> ~A.

Now let's look at the remaining premise.

~X ->J

How do we convert X to ~X. We can use a contrapositive again:

X -> ~A is logically equivalent to A -> ~X

We can combine it with premise (2) to form the following chain:

A-> ~X -> J

which is the same as:

A -> J

This statement is logically equivalent to its contrapositive:

~J -> ~A

Hence, the properly inferred conclusion is either:
A -> J or ~ J -> ~A

Let me know if you have any further questions.