"Cogent" has a specific meaning in the study of formal logic. I would recommend becoming familiar with as many formal logic words and concepts as possible while preparing for the LSAT.

This definitely didnt feel like a 2/5

All cats are mammals.

That animal is a mammal, therefore it must be a cat.

Cat→Mammal is correct. (If it is a cat, then it is a mammal)

Mammal→Cat is incorrect. (If it is a mammal, then it is a cat.)

Do you see what is wrong with the reasoning when you mix up the sufficient and necessary conclusions?

Being a cat is sufficient for being a mammal, but it is not necessary.

There are plenty of other types of animals that can be classified as a mammal. Bears, giraffes, and whales are all mammals.

I also made this assumption, which is apparently wrong. I assumed that Penn appearing in the conclusion would imply that he was eligible based on record but failed some other requirement.

The piece you're looking for is the comparative claim in the stimulus. "More likely now than it was five years ago" is comparing conviction rates in two different times. So the stimulus says there are less car thefts overall, but more convictions. This is the discrepancy which needs to be explained. One would naturally assume that more car thefts would equate to more convictions, but this is the opposite of the phenomenon described in the stimulus.

I also interpret "vacuum tubes" as a superset. The rule applies to all vacuum tubes, including the small experimental vacuum tubes.

It would be irrational for the writers to assume that we know about the nature or size of vacuum tubes in general.

This one was pretty clear cut for me. The stimulus says in ALL other significant respects. Even if there were 100 other significant respects, missing even one would make them not preferable to semiconductors. So even breaking ONE of those rules (not matching max current capacity) disqualifies the vacuum tubes entirely.

Was it a faulty assumption to assume that

decreased cost of living → more people living downtown → more traffic congestion → /profit increase

That seemed like a fair enough assumption to me.

I guess the entire last sentence is nothing but a trap.

The syllabus hasnt gotten to other question types which use comparatives and other lawgic concepts yet. This is simply identifying premises and conclusions.

When forming the contrapositive of a conditional relationship such as Z→REC, you must switch the sufficient and necessary conditions AND negate both of them in order to get an equivalent conditional relationship.

Thats what a contrapositive is- an equivalent conditional relationship, but expressed in a different (but logically equal) way.

This leaves you with /REC→/Z