Question on rules of inference

[cue928]

Homework Statement

What rule of inference is used with the following statement:
Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials.

I set this up as p = kangaroos live in Australia and q = kangaroos are marsupials. Therefore, p. To me, it looks like the "simplification" rule, but in our book, simplification is set up as:
p ^ q; therefore, p. Can I change how I defined p and q or am I wrong to begin with?

 

[Mark44]

Homework Statement

What rule of inference is used with the following statement:
Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials.

I set this up as p = kangaroos live in Australia and q = kangaroos are marsupials. Therefore, p.

Therefore q.

To me, it looks like the "simplification" rule, but in our book, simplification is set up as:
p ^ q; therefore, p. Can I change how I defined p and q or am I wrong to begin with?

If your hypothesis is p ^ q, the conclusion can be p or it can be q.

IOW,
p ^ q ==> q
and
p ^ q ==> p

 

[cue928]

Thank you.