Logical Reasoning

PT106 · S1 · Q20 If the economy is weak, then prices

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If the economy is weak, then prices remain constant although unemployment rises.

Statements

Conditional - "if" (left side) prices constant economy weak → and unemployment rises

Conditional - "only if" (right side) unemployment → investment rises decreases

When we're given conditionals, we check to see if they chain together. Is there a common ingredient? Sure, "unemployment rising".

We can chain that together to say: economy → unemployment → investment weak rises decreases

The other thing we check for with conditionals is to see whether any facts trigger them (or, more commonly, their contrapositives)

The fact that we're told investment isn't decreasing, means that we can derive the contrapositive inferences: - unemployment is not rising - the economy is not weak

Goal

The correct answer on Must Be False usually contradicts a conditional (trigger happens but outcome doesn't) or contradicts an inference we've made.

Look for answer that contradicts this,

economy → unemployment → investment weak rises decreases

or that contradicts one of these

- unemployment is not rising - the economy is not weak

20.

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

  1. Correct

    Either the economy is weak

    Why this is right

    "Either X or Y" means that "at least one of these two things is true". But we know that both of those things are not true. The paragraph told us that investment was not decreasing. That idea triggered the contrapositive of our chained conditionals: economy → unemployment → investment weak rises decreases which told us that the economy is not weak. Our knowledge that investment is not decreasing and that the economy is not weak contradicts this answer.

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

    45% picked this

  2. If unemployment rises, the prices

    Could Be True

    This answer isn't something we can infer from the conditional we're given, economy → unemployment → investment weak rises decreases + prices constant But the conditional we're given doesn't contradict this. To contradict this answer, we would have needed to know that there are times when unemployment rises but prices are not constant. We don't have any example like that.

    7% picked this

  3. The economy is weak only

    Must Be True

    "Only if" = right side, so this says economy weak → investment decreases That's a valid inference from the conditional chain we were given. economy → unemployment → investment weak rises decreases + prices constant So, this is the opposite of what we want on a Must Be False question.

    15% picked this

  4. Either the economy is weak

    Could Be True

    It's possible that prices are constant. When we learn that investment isn't decreasing, it triggers the contrapositive. economy → unemployment → investment weak rises decreases (+ prices constant) The contrapositive rules out unemployment rises and rules out economy weak, but it doesn't have anything to do with prices constant. We know the economy is not weak, but it's possible that prices are still constant. We knew that weak economy was sufficient to trigger prices constant. It never said it was necessary, so prices could be constant even when the economy is not weak.

    20% picked this

  5. Either unemployment is rising or

    Must Be True

    We derived that the economy is not weak, so this answer must be true.

    14% picked this

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