Logical reasoning PrepTest 101 · Section 2 · Question 24

Flawed

Strengthen with Necessary Premise Questions / Sufficient & Necessary Questions

Math proposition → ~Proven by observation

This is an interesting Strengthen with Sufficient Premise question, as it presents a conditional premise (“No…”) and a conditional conclusion (“any”), and that’s it.

Normally, we’d have a single conditional premise that’s then applied to a specific situation (and generally fails to show the situation meets the sufficient condition). Or we’d have multiple conditional statements that chain together, with a gap in the chain, or between the beginning or end of the chain and the conclusion.

Here, however, we just have a single premise and conclusion. They do overlap, however! “No” introduces a sufficient condition, and we then negate the necessary, which is how we got our diagram of the premise. And “any” introduces a sufficient condition, which is how we ended up with the diagram of the conclusion.

Since in these questions, we know we have to connect terms, we should know that the correct answer is going to need to connect ~Proven by observation and ~Know to be true, but we need to make sure we get the direction right. To do so, let’s start with the conclusion and see what we can build as far as a conditional chain is concerned:

Math proposition → ??? → ~Know to be true

Adding in our premise, we get:

Math proposition → ~Proven by observation → ??? → ~Know to be true

Since we’re out of premises, we should connect the terms that are on the two sides of the ???/missing part, and also take the contrapositive - so our anticipation of the correct answer is:

~Proven by observation → ~Know to be true

Know to be true → Proven by observation