Logical Reasoning

PT124 · S1 · Q7 Superconductors are substances

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Superconductors are substances that conduct electricity without resistance at low temperatures.

Given

Three of the four claims are conditionals, so we should be attracted to those and be asking ourselves whether any of them chain together or whether we can apply any of them to a provided fact (or both).

(1) Their use, however, will never be economically feasible, unless there is a substance that superconducts at a temperature above minus 148 degrees Celsius.

EF → M148

(2) If there is such a substance [one that superconducts above minus 148], that substance must be an alloy of niobium and germanium.

M148 → ANG

(3) Unfortunately, such alloys [alloys of niobium and germanium] superconduct at temperatures no higher than minus 160 degrees Celsius [not above minus 148].

ANG → ~M148

Evaluate

These three claims seem to chain together to give us this:

EF → M148 → ANG → ~M148

How weird! Within that chain of conditionals is a contradiction. What does that mean? If the trigger to a conditional leads you to a contradiction, then the trigger can't be true (because contradictions can't be true).

Goal

It looks like they are rewarding our ability to see ~EF, or "superconductors will never be economically feasible".

Let's look for that, or anything else we can derive from these facts.

7.

If the statements above are true, which one of the following must also be true?

  1. Correct

    The use of superconductors will

    Why this is right

    The first and second ~ANG → ~M148 statements imply that ~M148 → ~EF substances that are not ∴ ~ANG → ~EF an alloy of niobium and germanium are not economically feasible superconductors. The first and third ANG → ~M148 statements imply that ~M148 → ~EF substances that are an ∴ ANG → ~EF alloy of niobium and germanium are not economically feasible superconductors.

    Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.

    64% picked this

  2. If the alloys of niobium

    Contradiction

    The second and third ANG → ~M148 statements imply that no ~ANG → ~M148 substance [substances that are alloys of niobium and germanium and those that are not alloys of niobium and germanium] superconducts at temperatures above minus 148 degrees Celsius.

    3% picked this

  3. The use of superconductors could

    Contradiction

    The statements imply that the use of superconductors will never be economically feasible.

    10% picked this

  4. Alloys of niobium and germanium

    Contradiction

    Such alloys superconduct at temperatures no higher than minus 160, so they must superconduct at temperatures below minus 148.

    10% picked this

  5. No use of alloys of

    Too Strong

    This goes beyond using such alloys as superconductors. While such use will never be economically feasible, other uses of such alloys are beyond the scope of the statements and may be economically feasible.

    13% picked this

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