Cumulative level test: Formal reasoning: translating and testing arguments

Check understanding, separately from reading

10 questions · 80% to pass · no timer. This longer test revisits both units in the level. These authored questions assess recognition and application of the taught distinctions, not professional qualification. You may review the lessons and retry. Repeat attempts reuse the question bank; a remembered answer is not proof of transfer to a new situation.

Saving a lesson records reading only. Previous lesson completions have not been converted into passing scores. You can continue reading without a pass; the assessment remains unpassed.

Question 1

Let P mean “the archive is open” and Q mean “the manuscript is accessible.” The argument “If P then Q; P; therefore Q” relates two complete claims. Replacing P with “archive” would lose the assertion that can be true or false. Before evaluating the argument, write the key for both letters.

Question 2

A reading requirement says “submit a commentary or a translation.” Under inclusive or, submitting both satisfies it. Under exactly-one instructions, both violates it. The cases P true/Q false and P false/Q true satisfy either rule; P true/Q true is the case that distinguishes them.

Question 3

Formalize “If the seal is broken, the indicator is red.” A broken seal with a non-red indicator refutes that conditional. An intact seal with a red indicator does not: another mechanism might make it red. The formula alone says nothing about that mechanism.

Question 4

If a file is encrypted, it is unreadable without the key. This file is unreadable. Concluding that it is encrypted overlooks corruption. A corrupted, unencrypted file makes both premises true and the conclusion false. The problem is the inference, even if this particular file later turns out to be encrypted.

Question 5

If a shape is a square, it has four sides. A triangle does not have four sides, so it is not a square: modus tollens. A non-square rectangle still has four sides, showing why “not square, therefore not four-sided” fails.

Question 6

“It is not the case that both witnesses signed” is compatible with one signature. “Neither witness signed” excludes even one. If Ada signed and Ben did not, the first assertion is true and the second false. That single case prevents treating the phrases as equivalent.

Question 7

Consider P or Q; not P; therefore Q. To make the conclusion false, set Q false. The first premise then needs P true, but the second needs P false. No assignment meets all requirements. Contrast P or Q; P; therefore not Q: setting both true is a countermodel.

Question 8

In a domain of library items, “all manuscripts are catalogued” means any item that is a manuscript is catalogued. “Some manuscript is catalogued” additionally requires a manuscript. A library with no manuscripts satisfies the universal conditional but not the existential claim.

Question 9

In a two-person domain, Ada trusts only Ben and Ben trusts only Ada. Everyone trusts someone. Nobody is trusted by everyone, because neither trusts themself. This relation satisfies the first statement while refuting the second; no claim about actual human psychology is needed.

Question 10

Thesis: every permissible policy is popular. One permissible but unpopular policy would refute it. That refutation would not show that all permissible policies are unpopular. Conversely, refuting “a permissible policy is popular” requires showing there is no such case in the specified domain.

Continuing does not mark this assessment passed.